There is a lot of great practical content in the answers so far. I would just add on an emotional level that:

• Whether it's the right thing for your business or not, when you fire someone, you are inflicting significant pain on another human being. This shouldn't make you change your decision but it should make you understand the gravity and do it with compassion. This person will have to go home to their friends and family and explain what happened and it may affect them significantly.
• You hope it won't affect them. You hope that they'll "bounce back" and that this will be "better for them" but it may not always be the case. Understand that. Don't be scared away by it - but understand it.
• Some friends will try to make you feel like you did the right thing for the person that was terminated. Perhaps that will be the case. But keep it clear in your mind that you did this for your company - not for the person who was fired. And accept the implications that come from that.
• You will likely feel bad (if you have empathy). And you should - it's a human feeling to have. Again, that shouldn't dissuade you from doing it, but by no means should inflicting pain on someone else ever feel good. Sometimes the correct course of action isn't one that will make you feel good. In the long run, you may feel good that you made the right decision for your company, but in the short term, it will suck.
• I personally think everyone that ever has to lay someone off should watch George Clooney's "Up In the Air" (http://www.imdb.com/title/tt1193138/). It really hits on a lot of the issues involved.
• All that being said, I'm not trying to change your mind on your decision. Your decision should be made based upon your intuition, the facts and some of the advice above. But understand that leadership decisions are tough for a reason. If they were easy, anyone could do it. :)

Good luck and be compassionate.