After escaping from the doomed Ceres Station, Samus tracks Ridley to the Space Pirate's fortress, Planet Zebes. Once Samus lands down on the surface, she'll exit her ship and your main adventure will begin. This first area drenched with acid rain is Crateria, from here you'll have to make your way down to Brinstar.
Go left past your ship, eventually you'll reach a door leading into a cave. Go through and head through the enclosed cavern. Eventually you'll reach a hole in the floor, drop down to the very bottom of the shaft and go through the door set in the floor.
You'll now find yourself in the same shaft that Samus escaped Zebes via in the original Metroid, and it'll be obvious because the place will look a complete wreck. Drop down to the bottom of the shaft and go through the door. You'll find the remains of the Mother Brain in this "Old Tourian" area. Go through to the door on the right to find an elevator in the next room. Ride the elevator down to Brinstar.
Once you land, go left to find the Morphing Ball, then head right into the next room. Grab missile no. 1 (Brinstar) down below the shaft, then go into the corridor on the right at the top of the shaft to find missile no. 2 (Brinstar).