You can ride your Pokémon by equipping it with a custom mount (/recipebook Mount).
There are 3 types of mounts: land mount, surf mount, and fly mount. Each Pokémon can only equip their corresponding mount type. Once the mount is equipped, you simply right click your Pokémon to ride it.
Fly mounts require a lot of gold, which can be found more often in the Mesa (Badlands) biome.