BREATHE!!!!!
I was working at a mall one summer when a guy came to my store and tried to make a large purchase with a credit card with a very clearly female name on it. I caught it and called the police... But you know what? He had been to 18, yes, 18 stores before mine and no one caught it!!!!! The card was just about maxed out.
It happens, stores have insurance and stuff to cover things like that. Theft of all kinds is also built into the prices that we pay for everything.
It all comes with time and practice. I don't know anything about any currency outside of the US but here there are web pages and things that can show you quick ways to spot a fake.
I was also a manager for a while and while you get upset when these things happen you know they are going to happen... It is just part of the job. A good manager will help you learn the quick ways to catch a fake and move on.
As for confronting people when it happens, I often made an excuse to call a manager out to do that That is until I was the manager