I had a petty theft case dismissed. The only thing that shows up on a background check is that there was a theft case dismissed. Do I have to be honest about what exactly happened and will employers find out about the details of the case?

Depends on what they ask you. If they ask whether you were convicted of anything, unless there is another conviction for something, you could truthfully answer "no".

It is possible to find out that you were charged, depending on how hard they look. If the charges were dismissed without a trial, it might be more difficult to find out those details. But be truthful if you are asked.