First, why did you leave? NEVER PUT because of supervisor conflict, or that you had some type of problem with authority! YOU WILL NOT GET HIRED.
Next, if you were fired just tell them. They will call your past employers anyway, so they might find out and if your lying it looks really bad.
If you did something illegal and got fired they will more than likely find out from a background check, unless your still going to court with the issue or if the charges got dropped.