If I were in this situation, I would have to rely on what I had already done in the past. If I were at the point of terminating an employee and had not already set up and followed various procedures, I would be in trouble. You cannot do a good job of terminating someone if you do so on the spur of the moment.
Any firm needs to have procedures in place that govern how discipline and termination will be carried out. They need to specify the sorts of actions or inactions that can cause a person to be disciplined. They have to specify the number of times that an employee can be disciplined before being terminated. They need to specify the sorts of steps that will be taken to inform the employee of what they have done wrong, to counsel them, and to let them fix their mistakes.
When an employee makes mistakes, you as the manager must make sure that you follow the disciplinary procedures to the letter. You must make sure that you keep all the necessary paperwork. If you do so, you will have proof that you are firing the person for a good reason and in a way that is consistent with written policies. Only if you do these things can you feel confident about terminating someone without legal repercussions.