Unless you own the company, every team member has a season that ends.  It often comes after a time that's been frustrating, confusing, stressful.  You've had long emotional talks with the team member.  You've changed or reduced their workload.  And yet, the situation hasn't really gotten better.  It's time to stop the struggle and it's your job to deliver that news.

A few things I've learned that have had a positive impact on the person who is about to be told their season here is over.

1. Make the call earlier than you want to:  The time to make the call is as soon as you, the leader, genuinely lose hope that more time is going to give us a dramatically better result.  Waiting makes things worse.  Waiting exhausts everyone involved in an unhealthy way.  Waiting results in relational damage that goes beyond the job.  
2. Have the right people in the room:  Have the right 3 or 4 people in the room.  Make sure they are there early.  Don't be too jovial beforehand.  Include any direct leaders involved and maybe someone that your team member might want to be in the room with them if appropriate.  
3. Be succinct and brief:  Be sure the team member knows why we are meeting to avoid feeling ambushed.  Briefly review the conversations and actions we've taken in the weeks leading up to today.  But this is no time for sermons or lessons.  Once a person hears that they are being fired, they go into a mild state of shock and don't hear much else you say after that.  This conversation isn't rushed; but it should not take more than about 5 or 10 minutes to deliver the decision along with any important details like a severance.
4. Be kind:  The time for candor and hard truth has come and gone.  The decision has been made.  The conversation to follow in this meeting should be very kind, very confident in order to avoid thrashing and last ditch negotiating from your team member, and honoring.  You honor the person by bringing up some of their highest achievements and contributions to the business.  You emphatically state that this decision does not erase the good things they've done and how they have permanently impacted your culture for the better.  

If they are emotional, offer to step out and allow them to compose themselves in your private office for as long as they need.  Walk them out caringly.  You can do the paperwork in a few days.  Your job now is shifting from being their leader to just being their friend.  Do it well.