Since my name has been mentioned here a few times...
I, sadly, have had to terminate the employment of several people. But these terminations take two forms.
1) If a person is being terminated for cause (e.g., lying on expense account or otherwise violating company policy), it is easy. You go to his office with someone from HR and security (always do it in his office, not yours), tell him why he is being terminated, tell him he has X minutes to clean out his office .. and have security escort him off the premises. (Obviously, you have cut off his email account prior to visiting him).
2) If it is an employee who just isn't hacking it anymore, it is more difficult. HR knows you are going to his office, but you do it alone. You have a nice chat. You thank him for all his contributions, but explain why it is time for the company to move on. You pick a date in the future for his last day, you give him an overview of the benefits he will receive and you let him vent and try to answer his questions. You let him know who will be his go-to person in HR. Then you usually wind up either hugging each other or shaking hands. My experience is ... It is never really a surprise to the employee in question. He has gotten enough signals to know he is not "hacking it." Oddly enough, some of the people I had to let go in this way... have remained close friends.