You could probably do an internet search of your state's private security requirements and find out.
If you bother to tell the potential employer, offer to take a drug test and suggest they test you periodically through a probationary period. This is assuming you are drug free. If you aren't, forget about it.
Also, it'll depend on the type of guard duty.
If its for an armored car company or something that involves money, expect them to ask if you've ever thought about how to rob them. Answer yes. Anyone who applies for those jobs and answers no is lying and will be overlooked.
Lastly, put yourself through some criminal justice and communications classes and any certifications you can (CDL, CPR, concealed carry if your convictions were misdemeanors, volunteer at drug court-style programs, volunteer or auxiliary fire fighter or police training, etc.).
Google Securitas if you're looking to work for something bigger than your local shopping center or mall.