What is the law regarding on-call pay?

Whether on-call (or standby) time is considered as compensable "hours worked" is determined by looking at whehter or what restrictions are placed on an employee. The factors to be considered include: the frequency of the calls; what the fixed time limit for response is; if there are geographic restrictions placed on the employee; whether the employee can trade their on-call responsibilities with another co-worker; and if, and to what extent, the employee engages in personal activities during such periods. If it is determined that the restrictions are too limited, then it will be considered time for which the employee must be paid.
At this point, you can check with your state's Department of Labor or check directly with an employment law attorney in your area.

If you are an exempt salaried employee, there is never additional pay for on-call time.
If you are an hourly employee, IF you are forced to stay at the employer's location while waiting for the call, such waiting time is work time and you have to be paid--including overtime as applicable (when working more than 40 hours in a week). Anytime the employer requires you to be someplace (e.g. at work) for the employer's benefit, that is work, whether you are actually "working" at the time or not.
But if you can more or less go where or do what you want while being on call, that is not work time and you don't have to be paid; in this event, you'd only be paid if and when the call comes in and you actually go to work--then you'd be paid for the time working or responding to the call, etc.
Of course an employer can voluntarily choose to pay you even the the law does not require it (e.g. on call time when you can go/do what you want), but that's up to the employer.