I have fired a few people in my small business. It is extremely hard since ultimately it is my call being the final decision maker. But it has to be done when it has to be done. Don't make it personal. You will know in your gut when it is time to let someone go. Everyone knows. If you have a team, they also know who the "could be fired" people are.

The most important thing you can do as a boss/leader who has the authority to fire is to not fire abruptly. Make sure that they are aware of their performance issue (in case they are not, mostly everyone is). Give them one or two chances if you think they could improve. Document and set more clear expectations. Let them know they are on a performance watch. If still no improvement, fire. Of course, depending on your jurisdiction, get legal/HR involved as needed before firing.

Don't make this personal or emotional. We feel bad as human beings but do what needs to be done for the team to function well. remember that bad performers also could demoralize a team. So don't be selfish by being nice. Be respectful but do the right thing for the team.