After you get the Spazer Beam, you can get the Hi-Jump Boots and continue on to the next boss, who is guarding the Varia Suit.
Get the Hi-Jump Boots
After you arrive in Norfair via the Brinstar-Norfair elevator, go to the bottom of the room. Don't shoot through the floor yet. There is a door there, but it leads to a room that is too hot for you to safely enter yet. Instead, at the two doors that face each other near the bottom of the room, you can use the bottom-right door if you want to save the game, but beyond that, there is just a dead end (for now). If you save the game, go through the door on the left afterward.
Shoot the door on the left with five Missiles, then go through it. Take the Energy tank, then walk on the left side of the platform to break open some pit blocks. Roll through the tunnel, and go through the door at the bottom. Shoot the upper part of the wall and jump to the Chozo Statue, which is holding the Hi-Jump Boots. After you get these, you can jump far enough to get over the wall here and leave the room.
Be sure to kill the Geemer in this room to unlock the exit door. Go up to the top of the room and roll through the tunnel to get some more missiles, then roll into the tunnel on the right and bomb it open, then go to the right. If the door is locked, look for the Geemer and kill it. Then go through the door on the right.
You can't do anything else in the Norfair area right now, so go up to the elevator and take the elevator up to Brinstar.
Go to the Next Boss
If you didn't get the Spazer Beam, you can go to the left from the elevator until you reach the water room with the Yapping Maws, then shoot the upper-left ceiling and jump up into the hidden area there. At the top, bomb the first block, then shoot the second one (if you bomb it, it opens a hole in the floor that drops you into the jaws of a Yapping Maw), then go to the right and go through the door to find the Chozo Statue that is holding the Spazer.
Back at the elevator, walk to the right wall and shoot a Super Missile at the right wall to open a hole. Go through it and jump to the upper-right, into the statue's mouth. Open the door and go through.
Shoot the floor beneath the door and go to the bottom of the area. The door at the bottom can't be unlocked until later, so bomb the wall to the right of that door and roll through the tunnel to find a door in the ceiling. Jump up through that door.
Kill the Kihunters in this room, and if you want to save the game, go to the right side of the room and drop a bomb in the notch in the floor, then roll through the tunnel and go through the door to reach the save room. Then exit the save room, roll through the tunnel and use a bomb at the end to get out.
Go to the middle of the room and shoot the damaged-looking floor to open a hole. Go down and then go through the door at the bottom.
You will need to kill all of the enemies in this room. Go to the right, kill the Space Pirates with your Spazer Beam, then go to the right while avoiding the spikes that come from the right side of the screen. At the rightmost side of the room, you will find a Mini-Kraid that is shooting the spikes at you. Use missiles or charged shots to kill him quickly, then go through the flashing door on the right (if it's not flashing, you have to kill more enemies in this room).
In this room, you can shoot the ceiling above the entry door to reach a door. Shoot the door with a Super Missile and go through to reach an energy recharger and missile recharger. Then exit the recharge room, go to the left, shoot the floor and go down below.
Go to the right, where you find the Deceased Soldier. To the right of that, there is a Gadora on the door. It is vulnerable to missiles when its eye is open. It will shoot energy orbs at you if you don't shoot it quickly enough.
After you kill the Gadora, go through the door. After a few moments, Kraid will appear.
Kraid
The inside of Kraid's mouth is vulnerable to missiles and charged shots. If Kraid's eyes flash rainbow colors, it is about to open its mouth. You can shoot Kraid to make it open its mouth, and sometimes it will open its mouth on its own. If this doesn't work, you may have to shoot its face or body when it is not blocked by its hand.
After you have dealt enough damage, Kraid will rise up to the upper part of the room, so you will have to jump up onto the ledges. Kraid will start throwing claws around the room. You can shoot the claws to get rid of them, and they might give you energy, missiles, or bombs. Kraid can also shoot platform-like projectiles from his chest, which you can either jump over or jump onto.
If Kraid comes too close, jump to the platform on the left to avoid getting damaged by touching him.
Get the Varia Suit
After Kraid dies, go through the door on the right to get the Varia Suit. With this suit, you can now safely enter the hot rooms in Norfair. You also take less damage. The Varia Suit does not protect you from lava or acid, however.
Get an Energy Tank
Exit the room where you got the Varia Suit, then go to the left side of Kraid's room and go through the door. Go to the left past the Deceased Soldier, and you can optionally shoot the left side of the ceiling again to reach the recharge room. Then exit the recharge room, go to the left, shoot the floor and go down. Go through the door on the left.
Kill the Mini-Kraid again, then go to the left and go through the door at the end. Go to the left and shoot through the ceiling and go up to the area with the Kihunters. Kill them and go to the left, and go through the door in the floor. Roll through the tunnel on the left and use a bomb at the end to get out. The door on the left is flashing. Go through. Kill the Beetoms with missiles or bombs, then shoot the left half of ceiling until you find a hidden Energy Tank. Jump up to take it, then exit the room.
Go back to Norfair
Go upward and shoot the ceiling on the left to open it, then go up through the hole and go through the door on the left. Go to the left and shoot the metal wall with a Super Missile to open a hole. Roll through the hole and go down the elevator to Norfair.