I'm 34 and an engineer. I started with a relatively small inheritance, took a high income career path, saved most of my disposable income, invested during good times, took a calculated risk on a tech start-up, and avoided big losses and boneheaded mistakes. My net worth is now just under $1M. It would be over $1M except for liquidation costs (taxes during stock sales) and recent education investments. Nearly all of my counted wealth is in cash and liquid securities.

[update]: At age 36, I did a tally while getting prequalified for a mortgage and found that I'm currently just over $1M.

Many of us answering this question, who didn't inherit millions, have similar philosophies, particularly about being financially independent, frugal with our expenses, and loving what we do for a living. A million is usually just a number to those that have it: see What does it feel like to make your first million dollars and how does it affect your personal relationships? I can't buy a home outright with $1M in my preferred cities. It provides some freedom and resources so I can do what I want to do and not be a wage slave.

For wealth accumulation, I stress is that it's often more important to avoid major mistakes than do things perfectly right. Ching Ho's answer to How should a 22-year-old invest his/her money? has some good examples: one major mistake can set you back a decade of savings, if not permanently killing your chances (and you).

Key aspects of my wealth growth:

Savings is income minus expenses. You should work on both increasing income and reducing expenses.

Get educated. If you want to make and keep money, you need to know how people have done it and are likely to do it in the future.

• Learn basic macro and microeconomics, accounting, personal and corporate finance, management, etc. Also pick up behavioral finance and psychology, mostly to learn how humans sabotage themselves.
• Study millionaires and billionaires, and understand how they made their money. But beware of survivorship bias: what percentage actually succeed on those paths?
• In general, beware of confirmation bias: if you only like hearing what confirms your beliefs, like 99% of humanity, you're digging yourself a hole. Always be on the lookout for evidence that you're wrong, then analyze the heck out of it. When the facts change, change your mind.
• Read the Economist and other reputed economics/business periodicals: most Americans' understanding of how the world works doesn't hold up under scrutiny. If you have a favorite or a sole news source, you're giving in to confirmation bias and are probably a drone of a political party (doesn't matter which: none will make you smarter or wealthier). You need to break that habit.
• Don't hold to any one financial pundit, even someone proven like Warren Buffett: everyone is wrong some of the time. I'm particularly suspicious of those that tell us what to do in their shows, books, and seminars: they make most of their money off the rubes that pay to watch. Do you really think you should trust them?
• Understand who makes the big incomes in the US (The Top 1 Percent: What Jobs Do They Have?) and the mechanisms that make the money. Sometimes the source of income is surprising, or the tax avoidance mechanism is critical. A few examples: ultra high-end restaurateurs often run their restaurants at a loss and profit on cookbook sales, a.k.a "food porn." Carried interest protects hedge funds and private equity firms from taxes. US presidents currently make $400k/year during their terms, but make a heck lot more from speaking fees afterwards. The way to bigger money is often not obvious.
• Study general critical thinking and logical fallacies. See survivorship bias and confirmation bias above: they're the most common mistakes when looking for a path to build wealth.
• Question all assumptions, think about how they might be broken, and how you could profit by breaking them. Disrupting "the ways things are done here" or "the ways things have always been done in the industry" are how many companies made it big, from McDonald's (serving style) to Facebook (yet another social web site, but better) to DropBox (yet another file sharing mechanism, but better) to Zappos (great customer service that still doesn't quite make sense to me).

Choose college and major as an investment: high earning potential at a reasonable cost.

• Don't try to study something you hate or aren't good at, because you won't graduate.
• Go to a high ranked program at a highly reputed school (ideally top 5 in the world, but that's increasingly chancy), to gain skills/knowledge/connections that are directly applicable to an industry that pays extremely well and has a shortage of highly skilled workers (e.g., finance or tech). Some will argue that they get the same education at a lesser school, but you won't get the same reputation, connections, and network.
• A master's or other graduate degree is often worth the additional investment and sometimes necessary for a profession (e.g. medicine, law). Besides the experience, it signals you as being the best. I obtained a top-5 PhD in computer engineering, and it set me back in terms of hitting $1M quickly (6 years of low income), but it did open doors that I hadn't anticipated and got me some years back that way. An extreme example is a friend that quit being a professor at a top school and made his first $1M in an extremely short time at a high frequency trading firm.
• The education must be cheap relative to the earning potential it provides, or paid by someone else. It's a bad investment if it costs more than it makes.
• Professions and their earning power change over time, so be very careful with your assumptions, especially when trying to go off of your parents' generation. Many medical doctors now go into deep debt and don't make the money they used to. The market for many paralegals and some lawyers has been replaced by the Internet, plus lawyers currently have an abysmal career satisfaction rate. MBA programs have proliferated and aren't as valued as they used to be.

DON'T LOSE MONEY. Perhaps the most important idea: avoid catastrophic events, financial or otherwise. If you lose 90%, you need to make a 900% profit to get back to break even. It's very hard to recover from major losses.

• Once married, stay married. Divorce is one of the greatest wealth destroyers in the developed world. Get a prenuptial if there's any question; there shouldn't be a question, but you should probably get one anyway. If you marry, marry someone even more frugal than you and wants to build wealth with you. My wife had no financial assets when we married, but I don't have to worry about her spending a couple thousand every week on purses and shoes. I even have trouble trying to get her to take vacations or eat at sit-down restaurants.
• Avoid risky/adolescent behavior that can result in lawsuits or being charged with/convicted of crimes: driving fast through residential streets, getting involved in physical fights, or having one night stands (Kobe Bryant). Even if you don't get a criminal conviction, legal action in civil courts can destroy current wealth and block you from future wealth. (O.J. Simpson.) And there’s always the chance that it might kill you (Paul Walker).
• If you care about money more than children, do not have children and do not do anything that might cause you to have children. If you want children and don't already know that they're the biggest time and money sink you'll ever encounter, you're fooling yourself. I would have hit $1M years earlier without children.
• Avoid remotely questionable or unsafe investments, like the vast majority of restaurants. The same goes for investments in fickle markets, like most collectibles.
• Don't buy expensive consumables if possible. They're usually valueless when used, or depreciate quickly (new cars).

Don't be delusional. You need to see reality as it is, not as you would want it. (Remember confirmation bias?) Most people do the latter and plan and live by wishful thinking.

• The vast majority of people want to LOOK rich, not BE rich. The two are opposites: the first requires spending money, and the second requires saving it. Don't pretend that they aren't counter to each other.
• If you expect to work 40-hour weeks or less, you will probably be out-competed, and at the very least you're leaving a lot of profit uncollected.
• Know your probabilities and statistics. Lotteries are statistically the same as burning your money, as far as your profit is concerned. You're probably more likely to slip and crack your head open, die in a car accident, drown, or be murdered TODAY than EVER make big money as a novelist or artist.
• Know what the standards are. When polled, 80% of Americans believe they're above average in many different fields. It's because a lot of them have no clue what average is: some names for this are Illusory superiority or the Dunning–Kruger effect. That extends to the standards of the fields you're trying to compete in. A man thought he was "good at math" because he could balance his checkbook, thought he could be an engineer, and failed remedial geometry, long before reaching the three semesters of calculus and several other math courses most engineers take. A man who thinks he's tough may not make it through military basic training, let alone the Special Operations schools.
• Online degrees have reduced value over traditional degrees, especially when awarded by paper mill universities: look at the income of graduates. Even if they provided the same education, what matters is that employers see and pay you differently.
• College: not everyone wastes their college years partying and "discovering themselves." While you're out getting drunk, someone else is studying their rear end off, both in school and how to increase their wealth, and doing their damnedest to beat you to those lucrative jobs. Like every other opportunity, use it.
• Murphy's Law in all its forms. If you're employed, you will be laid off when you don't expect it or can least afford it. No job is safe.
• Risky behavior that has a very small chance of resulting in death or permanent impairment can and will screw you if you do it long/often enough: see Jared Diamond’s Guide to Reducing Life’s Risks.
• Education never ends. I'm always reading and studying.

You have to be stone-cold realistic about your current situation and your odds. Then you can start to change both.

Inherited seed money. Don't squander windfalls of any kind. I received about $100k, intended for my education, that I could keep afterwards because I didn't overpay for my education. I was lucky and fortunate, and I made the most of it. Inheritance and connections are how many of the truly rich become rich: http://www.businessweek.com/articles/2013-04-22/how-did-the-worlds-rich-get-that-way-luck.

Passive and/or multiplicative income. I invest my money, and it makes more money while I work on my day job and secondary projects. Businesses hire people to create more value than they cost in compensation: that's how they make a profit.

Maximized my contributions to tax-sheltered retirement accounts. I've done this every year since I started earning money: sometimes only an IRA, sometimes a 401k. The tax-free compounding helps over the long run, and it lets me liquidate those assets without tax consequences in special situations (see the next topic). It's maybe a third of my net worth.

Avoid or mitigate the major stock market crashes (DON'T LOSE MONEY).

• I shifted a significant part of my investments out of equities in both 2000 and 2007 because I thought the stock market and the people participating in it were insane. I was able to avoid much of the potential loss during the subsequent crashes, and jumped back in when everyone else gave up. Avoiding crashes when you're investing is hard, but the main thing is to avoid the cliffs, not attempt to time the peaks. Ken Fisher, billionaire and Forbes columnist, is better than most at calling crashes before they happen. Note that even with crashes, it's often better to be in the market. I was lucky with my timing.
• Some business owners avoid the stock market entirely and plow profits back into their businesses. It's a different set of risks, but "Put all your eggs in one basket, then watch that basket." [Edit: Warren Buffett is famous for this quote today, but the quote is originally attributed to Andrew Carnegie, and was borrowed by Samuel Clemens/Mark Twain for his writing.]
• There are always risks you can't control, particularly the economy-wide ones that damage everyone and everything. Diversify enough to avoid being wiped out completely, and never give into the euphoria or malaise that infects others. Be different (see below).

Business ownership. The very rich own businesses. Being paid a salary means that someone else is paying you money to make even more money for them. Actors and musicians don't reach anywhere close to the heights of entertainment wealth until they create their own businesses (Oprah, Jay-Z & Beyonce). I was in the first 10 employees of a tech startup, owned a few percent of the company, and received a payout and retention bonuses when it was acquired. That's the source of about a third of my wealth.

Think long term. It took an extra year or two to become a millionaire because I paid for my wife's MBA from a top school. Tuition + two residences + plane flights + miscellaneous travel cost a few hundred thousand dollars. But she started making more than double what she used to immediately after school and her earning potential is far higher than it was before.

Be different. Most people are afraid to be different, but in order to be "better," you need to be different. Doing the same thing as almost everyone else is, by definition, average or mediocre. (However, being different doesn't automatically make you better. More likely you're just crazy.) Be unconventional, but do it for logical reasons. I do different things all the time, usually by breaking poor assumptions.

Always keep developing and looking for opportunities. There are always people with more money, free time, speed, motivation, energy, experience, intelligence, skills, connections, or anything else, compared to you. You have to compete hard, fast, and smart. You have to leverage whatever advantages you have, fix anything that's unacceptably weak (social skills for many engineers), and keep building your assets, skills, understanding of your business and the world at large, reputation, and network.