At the manufacturing facility, regulatory requirements mean you need a specialized wind tunnel to perform testing. The big part of the testing revolves around aerodynamics and icing. Testing is done at cold temperature and high altitude conditions and involves, among other things, subjecting the device to solid ice particles and supercooled liquid water droplets in high concentrations.
On the flight line and local maintenance facilities, AOA's are usually tested along with the rest of the pitot-static system with RVSM (Reduced Visual Separation Minimums) test sets such as this one.
This all applies to commercial airliners and private jets, as well as military aircraft. Most general aviation propeller-driven aircraft do not have AOA sensors or indicators, but you can buy third party systems and install them if you wish.