I don't like using terms like "fire" or "terminate." To me they have too much emotion attached to them to be appropriate when splitting with an employee. I like to say that "fred was asked to leave the company" or "fred, we need you to leave the company." That works better for me and, I think, it also works better for the person who is being asked to leave the company.
But more than how to say it, I think how you do it is paramount. Here are some simple rules along with some color commentary on each:
1) Be quick - once you've made a decision to let someone go, move quickly to do it. Don't procrastinate. Do get things buttoned up (terms of departure, departure date, how it will be communicated, etc) but once you've got things in order, have the conversation.
2) Be generous - Unless the employee has acted in extreme bad faith or done something terribly wrong, I like to be generous on the way out. I like to give some severance even if it is not required by company policy or contract. I like to vest some stock that may not be required to be vested. I like to paint the departure in as favorable light as possible. And I like to say good things about the person once they are gone. I like to be generous in financial terms and emotional terms. It makes things go easier for everyone.
3) Be clear - Do not beat around the bush. Start the conversation with the hard stuff. They will be leaving the company. Be clear about when and how. And be clear about the financial terms and other aspects of the separation. Do not mince words and do not say confusing things. Most employees in this situation will ask for reasons. Have them lined up in advance and be clear and crisp when describing the reasons. The reasons for a split do not have to be the employee's fault. They can, and often are, the company's fault. In startups, employees are almost always at will and it is the CEO's right to ask anyone to leave the company for any reason. So just be as honest as possible, be clear and crisp about the reasons, and don't turn this into a long involved discussion.
4) Get advice - There are some situations where the company has some potential legal exposure in these situations. When you are a small company, ask your lawyer about the specific situation so you know when you have one of them on your hands. When you are a larger company, your HR team should know when you have one of these situations on your hands. But make sure you are appropriately advised about a departure before sitting down and having the conversation. In the off chance you have a tricky situation, you will need to handle it differently and you will need advice on how to do that beyond what is written in this post.
5) Communicate - Once the employee has been told about their departure, you should immediately communicate it to those who will be affected in the company. For executives and co-founders, that means the entire company. So figure out how you are going to have that conversation immediately after you have the conversation with the departing employee. Be consistent with your messaging. Don't tell a departing employee one thing and the team another. People talk. And they will quickly figure out that you are spinning, bullshitting, or something worse if you give different messages.
When an employee is asked to leave the company there are two constituencies you need to think about. The first is the departing employee. The second are the remaining employees. How you deal with the departing employee will be noticed by the remaining employees. Even if the departing employee was not liked, a bad cultural fit, or worse incompetent, the remaining employees will have some empathy for them on the way out and if you handle it well, that will send an important message to the team. I find that a lot of inexperienced managers miss this nuance and it hurts them. They think they need to "look strong" to the team. They do. But they also need to look fair and humane. This is a big opportunity to do that.
I will finish with a few words aimed at the boss' own psyche and then suggest some further reading on this topic.
Asking someone to leave the company is never easy. I don't know anyone who enjoys doing it. But it comes with the territory. You don't have to learn to like it, but you have to learn to do it well. The thing that helps me and, I believe, helps everyone in this situation is knowing that you are doing the right thing for the company, the remaining team, and all the stakeholders in the business including customers, partners, investors, etc. When you put it in those terms, doing this unpopular chore becomes a bit easier.
If you'd like to read more on this topic, I think Ben Horowitz has written well on this subject a few times. I found these links below from Ben's writings and would encourage you to go and read them.
Preparing To Fire An Executive
Demoting A Loyal Friend
Lies That Losers Tell