You have to take the Helix or Dome fossil you found in Mount Moon to the Cinnabar Island Pokemon Laboratory. You can also take the Old Amber the scientist gives you in the Pewter City's Museum back door. You need HM01 (Cut) to get to the museum's back door.
Helix gives you Omanyte, evolves into Omastar at level 40.
Dome gives you Kabuto, evolves into Kabutops at level 40 as well.
Old Amber gives you Aerodactyl, no evolution in this game (Mega Evolves in Gen 6, 7 and Gen 3 remakes)