when someone accuses you of something and you know you are not guilty what can you do to make them believe you

The best you can do is tell what really happened, prove it if you can, and walk away. Sometimes you have to give people time. We all know how hard it is to admit you're wrong. They may eventually acknowledge that you are right or they may just start acting like it never happened. Some people need to be right so badly that they'll stay mad even when they know they're wrong. Once you've made your case, you just need to know you didn't do anything wrong and see how they decide to handle it.

Walk away knowing you are not the perpetrator.

Why? No point engaging in a "let me convince you" conversation as this is mentally tiring and very frustrating, and will more than likely prove pointless anyways. If somebody with narrow-thinking unfortunately has decided you have acted in a certain manner, no amount of words or counter-arguments will change their mind.

And even though this might not be the case, people who believe they must defend their honour/stand and fight, will come off looking defensive and unsure in the eyes of many so another good reason not to engage.

Our justice system is predicated upon the idea that you can never prove innocence, on guilt. Like trying to prove a thing does not exist. So all you can do is tell this person the truth and maintain your innocence. It's up to them, to believe or not.

when someone accuses you of something they had better have some proof. just tell them you didn't do it and leave it at that. you don't have to convince them.

First of all you have a clear conscience. Good.

Just say nothing at all and pray for justice to be brought forward.

Give them proof to prove and show that you are innocent.