Double Jeopardy isn't just the title of a flick (imdb.com rating, 6.0/10).
It means you can't be tried twice for the same crime unless your trial gets messed up, or the jury couldn't make up its mind, or you ask for a new trial (like if they find you guilty the first time).
Another protection is that you can't be forced to testify against yourself. It's called "taking the fifth" (5th Amendment). The judge will tell jury members not to think you're guilty just because you remain silent.
How many TV shows have you seen where the police read somebody their Miranda Rights? The Supreme Court ordered that suspects must be told: You have the right to remain silent... anything you say may be used against you in court...etc.
The Fifth Amendment also calls for Due Process of Law which means the government has to play by the rules.
Another big deal is Ex Post Facto. You can't be charged for doing something before a law was passed to make it illegal. So hurry up and commit your crimes now, before it's too late.
A Bill of Attainder is when the authorities make up a special law that applies only to somebody they can't stand. Definitely unconstitutional! Even though suck-ups appointed to student governments try it all the time.