FCC
The Federal Communications Commission (FCC) has issued six types of license operator class, each authorizing varying levels of privileges. For the purposes of operating FPV you’ll need the lowest class of operator, Technician.
The privileges of a Technician Class operator license include operating an amateur station that may transmit on channels in any of 17 frequency bands above 50 MHz with up to 1,500 watts of power. To pass the Technician Class examination, at least 26 questions
from a 35 question written examination must be answered correctly. Technician Class licensees also have privileges in four amateur service bands in the HF range (3-30 MHz).
No license is required for 2.4GHz or 900MHz in the USA, but only if you use extremely low power levels (0.5mW or less). A license is required for 500mW-1W, commonly used for FPV because of the increase in range.
More information can be found on the AMA and FCC websites:
(AMA)
Academy of Model Aeronautics
(FCC)
FCC: Wireless Services: Amateur Radio Service: Amateur Home