Up until ~ the 1960s, fonts were metal type.

Prior to the 1890s, the originals were made by directly cutting metal punches using metal tools: engraver, counterpunch, etc. So the type designer was working with a reverse image! Type could then be cast from the originals.

But at that time, the Linn Boyd Benton’s invention of the pantographic engraver allowed type design to happen on paper, and tracing the paper to cut metal type at a smaller size. But still, plenty of type design was done by a person cutting punches, and there was a certain amount of interpretation by that person. (See Hermann Zapf’s tribute to August Rosenberger, for example.)

The Monotype and Linotype companies with their own proprietary machines, also in the same time period, had their own type design approaches, but these would have been based on the above two options.

In the 1960s, type transitioned to phototype, and became letters on film! Type design involved drawing letters on paper which were then transmogrified to film. Existing libraries of metal type were converted to film by a variety of means.

In the late 1980s and early 1990s, type design transitioned to digital. Sketching or drawing on paper became optional, although at first it was still the norm.

Although early digital fonts used bitmaps (made up of dots) to define their glyphs (representations of characters), almost all modern formats use primarily mathematical outlines of lines and curves to describe the shape of the letters. Such outline fonts (sometimes called vector fonts) have the advantage that the shapes are completely scalable to any arbitrary size, without losing smoothness or sharpness.

Today, about half of pro type designers sketch on paper first, and half go direct to digital. (Of course, if the typeface is especially calligraphic or hand-lettered, almost everyone uses paper first.)

Even if they later stopped doing it, most type designers who have ever learned and used sketching agree that it is extremely valuable as an educational tool. Much of type design has calligraphic roots, at least in part, and sketching helps understand this. This is probably why both sketching and calligraphy are a standard part of all or nearly all higher education programs in type design (University of Reading in the UK, KABK in the Hague, and I assume at Cooper Union in NYC).

Personally, I suck at sketching, so I rarely do it in actual projects. But that’s not disrespect for its utility, and I still teach it in intro type design classes of 2.5 or 3 days. I would never abandon teaching it to beginners… unless the whole class was two days or less, perhaps.

Once on a computer, most type design happens directly in a font editing program, as it offers features specific to type design that one does not get in drawing programs (such as control of spacing), and has drawing tools optimized for the purpose.

Dedicated drawing programs such as Adobe Illustrator, while great for general-purpose drawing, are poor substitutes for type design programs as far as drawing glyphs for a font. Nearly all full-time type designers do the computerized parts of their drawing directly in a font editing program, rather than a separate drawing program.

My former company, FontLab (font editors and converters) makes a broad spectrum of such tools, from inexpensive (TypeTool) to professional (FontLab). Others worth noting are the open source FontForge (Mac/Win/Linux, but a bit of an antique, and uses non-standard UI on Mac and Windows), the easy to use Glyphs (Mac only), the limitlessly customizable RoboFont (also Mac only), Font Creator (Windows only) and the DTL FontMaster suite.

Many more tools are in development, but it remains to be seen which will become good options—these things have a tendency to get abandoned along the way. Making a full-featured font editor is a lot of work, especially if one wants to keep up with more recent technologies such as variable fonts and color fonts.