Most crimes with few exceptions are eligible for expungement if the case was subsequently dismissed or nol prossed. The majority of any sexual related offense is not subject to expungement, nor a drug trafficking offense.
Many first time defendants are given a diversionary program option. If you complete the program, the state attorney will then dismiss the case. It could also be if the Judge dismisses the case based on for instance a suppression issue. Keep in mind that you only get this option ONE time. If your case is not dismissed but the Court withheld adjudication (did not convict you), you may be eligible to have the case sealed. A sealing will prevent the average person from being able to discover it. Keep in mind though that military, law enforcement and academia can still see it even if it is sealed. With an expungement, the records are actually destroyed. The link below is the statute itself with links to the offenses that prohibit expungement or sealing.
Our office does handle expungements and sealing. Sometimes the process is 2-3 months, sometimes as much as 6 dependent upon how backlogged FDLE is at the time of application.