A while back Chris Dixon had a good post on firing people. I shared a couple of my thoughts on the topic in a comment. I thought I'd post those thoughts here as well and add on a couple more. These are a few things I like to keep in mind when parting ways with an employee:

With very, very few exceptions the person is better off being fired. If you're considering firing someone, and you decide not to, they have very little chance of being successful at your company in the long term. And the situation is bound to get worse. It's better to get them off to another organization where they can shine. While it can be very painful in the short term, I've never seen someone get fired that didn't end up in a better situation within a year.
In another role, in another company, in another culture, the person you're firing could perform better than you or anyone else in your company. You're not better than the person you're firing. They're in a place where they aren't performing at their best. It could be the role, the industry, the company, even the management that's keeping them from performing at the highest level. Regardless, I believe it's always best to push that person to find a place where they can rise to the top.
With good management, a firing should never come as a surprise. I believe strongly in a culture of candor. If an employee is performing well they should know it. If they're not performing they should know it as well and they should know exactly what they need to do to perform better. They may be unable to perform better (either because they don't want to or they're not capable) but managers should lay out clear expectations for employees and clear consequences when expectations aren't met. So that when it comes time to make a change, it's not you telling them they're fired, it's an agreement that expectations aren't being met and it's best to move on.
Never, ever, ever speak ill of a terminated employee to customers, employees or anyone for that matter. For whatever reason, it wasn't a good fit. It's that simple. Leave it at that.
Even though I've broken this rule in this blog post, don't use the word "fire". Say "part ways" or "moved on" or "made a change". It's a small thing but these phrases are far more elegant and professional.