Firing someone is extremely difficult to do both on the side of the employer, and on the side of the employee (and sometimes contractor and intern). In many cases the founder may never have worked as a manager and has never fired anyone. They would have no frame of reference to help them navigate this emotionally intense process.
The first thing you should know as a founder is that if the thought occurs to you that you may have to fire someone, you are probably a few months late already. People find this process very difficult and thus they tend to procrastinate and rationalize. If you find yourself wondering if the time has come, the time probably did come 6 months ago.
The second thing you should ask yourself is whether this a performance based firing, a personality fit based firing, or a lay off? Those are very different things. If someone needs to be fired because they are not meeting your expectations or because they are being disrespectful to their teammates and causing a toxic team dynamic, that is not the same as the fact that their role has been eliminated because you restructured your organization, or you are running short on money. Here is where honesty equals integrity. If you need to fire them, fire them. But don't tell them they are laid off in order to avoid the hard conversations.
If you are really firing someone, the other question you should ask yourself is whether the person had been given any feedback along the way. If they are not performing well now, they were not performing well 3 months prior either. Did you give them constructive feedback and come up with a performance improvement plan? If not, then you are not being fair to them. This is the one situation where I think it might be reasonable to delay the firing so you can talk about the performance issues with the employees and see if you can fix things.
Suppose after all this, you really have to fire them. There are two things you can read to prepare yourself for your first firing (which will feel probably worse than being fired). First round capital has a blog post on this. Also there is a book called Difficult Conversations that is a very dense read, but gives you strategies to approach this conversation in a way that respects the dignity of your employee and doesn't make the experience any more difficult than it has to be for them.
No matter how uncomfortable you feel during the firing, just remember that this conversation is for the employee, not you. You will need to find a way to process your own feelings and put theirs front and center and make sure you take care of them in the conversation and subsequent exit interview.
Special thanks: Martin Trust Centre, MIT
Edit: Javier Rojas, 16/04/20