In the US, the Federal Communications Commission (FCC) makes the laws and enforces them for radio communications, not the FAA. The laws are contained in 47 CFR § 87.
Section 87.18 says, "An aircraft station is licensed by rule and does not need an individual license issued by the FCC" (the sentence continues with information not relevant here). So people in an airplane don't need a license to talk on an air band radio. You however are not in an aircraft, so in order to use an air band radio, you would need an FCC license.
In order to get an license to use the FCC's "Aviation Services" (the legal use of radios on aviation bands in the US), you would need to know exactly what kind of station license you're applying for. There are many different types of stations, which are all specified in detail. See 47 CFR § 87.5 - Definitions. I counted about 25 different types of station. Here are some examples:
Aeronautical advisory station (unicom). An aeronautical station used
for advisory and civil defense communications primarily with private
Aeronautical enroute station. An aeronautical station which
communicates with aircraft stations in flight status or with other
aeronautical enroute stations.
Aeronautical multicom station. An aeronautical station used to provide
communications to conduct the activities being performed by, or
directed from, private aircraft.
Aeronautical search and rescue station. An aeronautical station for
communication with aircraft and other aeronautical search and rescue
stations pertaining to search and rescue activities with aircraft.
The way to apply for any of the Aviation Services licenses (besides the basic aircraft station license for which no license is required) is to register with the FCC's Universal Licensing System (ULS), and then file a license application electronically there, which will be the equivalent of the old Form 601.
If you were to witness a plane crash, your radio on the ground may have a difficult time talking to another station on the ground, because of obstacles between the two antennas. Air traffic controllers might not welcome kibitzing "civilians" who aren't familiar with their procedures on their frequency. Calling 911 (emergency services) on the phone would probably be more appropriate.