dodothedizzy is incorrect.
Depending on which state you live in, it can be perfectly legal for 14-year-olds to work. However, there are standards that must be followed.
According to the Rhode Island's (one example) Labor Standards FAQ,
"What hours can 14-15 year old minors work and how many hours?
Not before 6:00 a.m. or later than 7:00 p.m. (except 9:00 p.m. during school vacations). Federal Law is not before 7:00 a.m. or later than 7:00 p.m. (except 9:00 p.m. from June 1 through Labor Day). Maximum hours in Rhode Island is 8 hours per day, 40 hours per week. Federal is 3 hours per day (school day), 8 hours non-school day, 18 hours per week (school week) and 40 hours non-school week."
What kind of work can a 14-15 year old do? What kind of work can they not do?
Permitted but not limited to: Office and clerical (including office machines), cashier, bagger, price marking, landscaping (no power-driven machines), cleaning, waiting tables, bussing tables, dishwashing.
Not permitted but not limited to: Manufacturing, mining, processing food or materials, laundry (washers/dryers), warehouse, construction, freezers, meat coolers, loading and unloading from trucks, railroad cars or conveyors, jewelry processing (by hand, or machine), bakeries (except strictly counter help), on any dock (public or private), dispensing gasoline, oil, any work in a car wash.
So, if you're looking at a restaurant, it's more likely to be a hostess/busboy/dishwashing job. Just try to find a family-owned place and they may ask for parental permission. But it is legal in most states.