Pikachu uses balloons to fly. This was first depicted in this trading card from 1997:
Since then, flying Pikachu have appeared in a variety of media, including in the intro to Pokémon Yellow, in multiple spin-offs, and on commercial aircraft. Pikachu with the move Fly have been released as event Pokémon in several mainline games, which is why Fly is a legitimate move in some generations. See here for a list of all its appearances.
A surfing Pikachu variant also exists.
