Around 8 years ago, when I had a small company with around 10 employees, I experienced a bad reality: terminating an employee!!
it was a while I wasn't satisfied with his efficiency, and he didn't seem to be enough responsible regarding his duties. So I decided to terminate his contract. I think I made as many mistakes as I could!
first of all, when I started the discussion I tried to look so familiar and friendly, I was trying to tell him every minute that I know how he is feeling, while I really didn't!
I also was not so brief. It took around 20 minutes to describe him the condition, and then, we just started to argue about the matter! I really didn't handle it...
last mistake I made, was telling him lies about his capabilities. I bet it was better to tell him his weaknesses. He didn't need my nonsense!
by the way, try to be brief in such cases, trust your reasons when you are explaining the situation, expect some cries and uncomfortable conditions and at last, never tell your employee you know how he/she is feeling. You probably don't!