Someone at my work went to my supervisor and accused me of an untruth, but I do not know who it is and I would like to press charges

If your supervisor won't tell you, I don't know how you would find out. Ask other employees.

But as far as the law goes, if your supervisor believed a lie and acted on it, you start with personnel. You go higher if need be. But if word just got out about something about you that isn't true but doesn't affect your standing with the company, you will have a very difficult time doing anything but telling anyone and everyone your side of the story. If it was so bad that your job was compromised, consult an attorney, but you will have to pay.

You 'press charges' for crimes and this is not a criminal matter. Slander/libel are civil court matters, not easy to prove, expensive to sue for, and get you nothing most of the time.

There are no charges to press. This was not a public declaration. The only way to deal with it is through your supervisor by proving it was untrue and requesting that disciplinary action be taken against the other employee.

What was being told about you at work.

How many people have found out?

How did you find out about it?

Did you talk to the supervisor about it.

Has it affected your standing with the company

What was the result of the lie - that would be my concern.

Anything legal follows that.