If you've been busted for a misdeamor criminal act, you can get it expunged. Which means you can get all your files back, including fingerprints and mugshots. It's as if it never happened.

How do you go about doing that?

First you have to be eligible. Typically this means
a) only one conviction
b) not more than 1 year in jail
c) finished jail term, probation, paid fines, and fully discharged.
d) conviction cannot be for violent, drug, or sex related crimes.

Then you just go down the to courthouse where you were convicted, and most of them will have a simple form for you to fill out. Some of the more backward courthouses, still require you to file a "motion" in the court because they do not have a form. If so, you find a sample motion on the internet, or you can go pay a lawyer.

After your records are sealed, a criminal background check will not reveal your previous conviction. Then you do not have to admit that you had a criminal record unless you are back before the court, or you are applying for a job that is a government job or a job that puts you in charge of children or vulnerable adults.
But, private background check companies can still have the old info in their data_base_. So you would have to ask them if they show your own record, and if they do you need to show them that it was expunged and they should remove the info from their data_base_.