Expungement is the process by which your police arrest and court conviction records are erased as if they never happened. Typically this is done for non-convictions, but in some states, under certain conditions, for certain crimes and after specified time frames, you can apply to get your record expunged. The courts are under no obligation to grant your request. Crimes that are ineligible for expungement may be eligible to be sealed.
Go to your local police station or a state police station and tell them you want your rap sheet. The police will fingerprint you and run your prints, then give you the rap sheet. It has all of your arrests and convictions, supervision, deferred sentences and probation from their jurisdiction. If you go to the state police station, it should show your record from every jurisdiction in the state.
Contact your county court clerk's office to find out if your convictions are eligible for expungement. Follow the process they give you and, if they are eligible, follow the instructions given to you by the clerk. It will entail, at the very least, completing forms, getting copies and forwarding them to the appropriate government entities, two of which will be the court that sentenced you, and your state police department.
Ask your county court clerk if your convictions may be eligible to be sealed, if they aren't eligible for expungement. In this case, law enforcement and certain other government entities can always get to your record, but it cannot be divulged to employers or potential employers. It also cannot be viewed by the public. The process is similar to expungement and many jurisdictions may use the same forms.
State law governs which records can be removed or hidden, but county courts direct the process. Each county court has control over their records, so if you were tried and convicted in multiple counties, you will have to go through this process in each individual county. Additionally, your local police department can only provide you with a rap sheet for crimes committed in their jurisdiction. If you have been convicted in other jurisdictions in the state, you should get your rap sheet from the state police department, which should give you your records statewide.