The easiest way to find a pokémon's Hidden Power type is to teach it Hidden Power and use the move on a Kecleon. Kecleon's Color Change will faithfully report your Hidden Power's type.

If you can't find a Kecleon, the next-easiest method is to use Hidden Power on a variety of pokémon and narrow down the possibilities. For example, if you take your Shelgon/Salamence to the Ravaged Path on Route 204 and use Hidden Power on a Geodude and a Zubat, and it's super-effective both times, you'll know your Hidden Power is Ice-type because that's the only type that's super-effective against both of them.