Mt. Moon is a two-floor cave filled with Rock and Ground-type Pokémon, as well as some unique encounters. Wild Pokémon include Zubat, Geodude, Paras, and Clefairy. Zubat can be annoying due to its 'Supersonic' move, which causes confusion. Clefairy is a rare find and can be quite powerful.
You'll also encounter several trainers, including Team Rocket Grunts! This is your first encounter with the villainous organization. Defeat them to progress. There are also a few items scattered around, so explore thoroughly. At the end of Mt. Moon, you'll have a choice between two Fossils: the Dome Fossil (Kabuto) or the Helix Fossil (Omanyte). Choose one; the other will be lost. You can revive these later in Cinnabar Island.