How do you know if an aircraft engine has a supercharger?
As Bianfable has pointed out, the C-130 Hercules does not have a supercharger or a turbocharger. No turbine-powered aircraft have them. Turbine engines do not need these forced-induction chargers since turbine engines compress the intake air themselves. It would be impractical to design a supercharger or turbocharger for them.
The easiest way to know if a piston-engined aircraft has a supercharger or a turbocharger is to check the aircraft’s POH. If one is not handy, you can look at the aircraft engine itself.
An engine with a supercharger will have an accessory belt (usually wider than the other accessory belts) attached to the crankshaft or flywheel. In older aircraft (WWII, Korean War, etc), the supercharger will be less obvious. These may even be chain or gear-driven. The application of superchargers in this case would be for large, powerful engines.
An engine with a turbocharger will have the exhaust manifolds converge down to one pipe. That pipe will feed into the exhaust turbine of the turbocharger. Although, the exhaust turbine might not be readily visible, the housing for the compressor impeller should be more obvious and may obscure the turbine. What would be more obvious would be the additional manifold piping and ducting.
If neither of the above are accessible, just look at the model name of the aircraft. Most modern small General Aviation aircraft manufacturers will want to advertise that their model is turbocharged. A manifold pressure gauge that goes beyond 30 inches of Mercury may be an indicator as well.