When you are convicted of a felony all of your rights as a citizen are revoked. This includes your right to vote. However, after you have served your sentence, many of your rights are restored to you, potentially including your right to cast a ballot. Depending on the circumstances of your felony charge and whether you still are serving any sort of punishment for it, and what state you live in, voting may not be out of the question.
Check your felony record to be sure that it exists. Check the copy given to you when you were sentenced, call the courthouse where you were sentenced or ask the police station if they have a copy of your felony conviction. You need to be sure that your conviction is on record before you assume that it's stopping you from voting.
Check your state's voting laws. States like Washington allow those who have been convicted of a felony but who have served the entirety of a sentence and paid all court costs and restitution to vote again, no questions asked. Other states may require you to petition the court to have your rights restored, and others may require you to eliminate your record.
Expunge your criminal record. Felonies are serious crimes, and not all of them can be expunged. However if you have served all of your time, paid all of your fees and lived a legal life after all punishments for at least 5 years then you have a good record of being a solid citizen. File a petition with the court requesting that your felony conviction be expunged based on your behavior. Once expunged, your rights will be returned to you as if the conviction didn't happen.