Legally operating a Jet Ski requires the person to complete a NASBLA-approved boating safety course and have a regular boating license.
There's not separate license for operating a Jet Ski and as long as you have a boating license to operate a boat on the water you can legally operate a Jet Ski.
I've operated a Jet Ski without a boating license before when I was younger and was never caught because if you go out somewhere where hardly any police are around then it's unlikely you'll be stopped and asked for the boating license unless you do something wrong to get the cops called on you.