There may be no “I” in “Team”, but there is one in “Fire”.
In this scene, from the iconic movie, Remember the Titans, Gerry Bertier, clearly demonstrates two of the most important aspects in firing an employee.
First and foremost, it should be your decision, and as a manager you need to take personal responsibility for such decision. Sometimes junior managers will get pushed into a corner by senior managers/department heads, etc. who want to dismiss someone from their team. Rather than go to bat for their employee they will sheepishly let them go, but tell them it wasn’t their call. Never pass the buck when firing an employee.
The second most important aspect is to do it personally. If you don’t have the ability to look someone in the eye and tell them they are fired, you probably shouldn't be in a position of management. (I will write more on this at a later point in time, but yes, no matter what the circumstance, it’s supposed to feel awful to have to fire someone. It’s called being human.)
One of my connections sent me an email from his boss, through which he was laid off. Apparently, his manager tried to reach him via phone and got his voicemail, so he sent him an email instead. The email stated he was under pressure from management to get through to everyone right away so that’s why he emailed him. The clincher was this line, “I really wanted to keep you but “Mike” made all the final cuts. You know how these things are…etc..” Classic…
There's a lot to cover on this topic, but two cardinal rules to start with are that when you fire someone, make sure it’s YOUR decision, and be sure to do it yourself, in person!