Brinstar is a main area of Planet Zebes. It is being divided to a jungle-like, lively area (upper Brinstar), and a silent, red-soiled area (lower Brinstar).
First Visit
Reaching Brinstar
Although it may seem like it isn't accessible from the get-go, Brinstar is the first place to go when arriving on Zebes. After you passed the old Mother Brain lair, an elevator leads to a deserted cave which seems to be not connected to the main section of Brinstar, though it actually is, as you will see when getting the Power Bomb upgrade. This place is the original start point of Metroid for the NES, where you can find the Morphball. See Crateria if you haven't gotten it yet.
However, you will be able to visit the main part of Brinstar after acquiring the Morph Ball Bomb from the Chozo Statue. After getting the bomb, battling the statue and leaving its chamber, go back the way you came until you reach the spot where you had to morph into a ball. Take the way on the right by climbing the steps and bombing away the blocks with your new item (
, as shown when getting it).
After leaving the tunnel, head left until you reach a wall made of violet-grey stones. You can simply blast this wall. Pass the gate behind it, and run through the cave. At its end, you will find your first Energy Tank. The next room holds green Space Pirates, which are immune to your standard beam. Use missiles instead, or, if you're insane, bombs should also work. When reaching the bottom, you can choose between two gates. Take the left one. The right door leads to Tourian, an area you will explore much later on.
Another corridor awaits you, which leads to the room that contains the elevator that will lower you down into Brinstar.
The first Room
The first room contains five gates. If you're interested in getting the Brinstar map, take the upper left gate first. When you reach a wall, place bombs at it to pass. After getting the map, you'll have to kill all the enemies to leave the corridor.
Thereafter, enter the opposite room. It contains a bridge that will collapse when you try standing on it. Try to fall down into the first "box" to get a missile container. Leave the box by placing bombs at the left wall (you can also enter the box that way). You can hardly cross the bridge until you get the Speed Booster, so exit the room. The middle left gate contains a save point. Save, if you want, and head for the bottom of the room. The left door leads to a a missile recharger. If you choose to get there, watch out for the firefly-like aliens. They can hurt you, but if you kill them all, the room will be completely dark.
Finally, take the right door as soon as you're finished.
Getting an Upgrade
After running along that shaft, you will arrive in a huge hall. Head for the upper part. As you arrive, you can see that the wall is thinner on the left side. You can reveal a save station by placing a bomb at the spot on the very left (→ picture). Save, and head right. You will encounter some mantis-like critters; kill them to get to the next room.
Fighting Spore Spawn
That next room is Spore Spawn's lair. It's a giant spore, spawning little spores that can hurt you. It will immediately start moving around the room. Morph into a ball during this phase, and dodge the small spores. As it stops moving, it will open its "mouth". Shoot a missile into it (your beam won't have any effect). Now, simply keep that strategy for the rest of the fight. The boss will become faster over time, but that doesn't really matter. If you run out of missiles, shoot the small spores and collect their drops. 10 missiles should be enough for this boss.
As soon as it's dead, collect its drops, jump up the vertical shaft above and pass through the gate. At the end of the following room, you will find a spawner pipe that does not spawn enemies. Jump on its top to make it collapse. You'll fall down a long duct and land in front of a Chozo statue holding the first Super Missile Container.
About Super Missiles
Super Missiles cause fives times as much damage as normal missiles, i. e. 1 super missile is worth 5 standard missiles. They can be used to easily kill enemies, and to open red and green gates.
Going deeper
After picking up the Super Missiles, head left and walk along the two rooms. As you encounter a green gate, shoot it with a Super Missile to get through. In the following room, a single stone will block your way. If you try to use a standard bomb on it, it will show you the icon of a Super Missile, which means that it can be blasted using one of those. When you've made your way through the tunnel, keep heading left until you reach a wall, then jump down and collect the Missile container.
The Charge Beam
Your first Beam upgrade lies beneath this container. Blast the two conspicuous stones on the right with a bomb and roll into the hole. As you fall downwards, a Chozo statue holding the Charge Beam upgrade will become visible.
Operating the Charge Beam
This part refers to standard controls. For further details, see Controls.
To charge up the beam, press and hold . To shoot, release again. The longer you charge, the more damage causes your shoot.
If you spin jump while your beam is fully charged, you can perform something like a "pseudo Screw Attack": you can cause damage or kill little enemies with this move.
By morphing into a ball with a charged beam, you drop five bombs at once around you.
Disintegrating Bridge
After leaving the statue's pit, pass the upper tunnel by climbing on the step above the hole, morphing into a ball and setting a bomb on the very right (→ picture (left)). Keep pressing 
all the time. As the bomb explodes, the force will carry you into the air. The next room holds a secret Missile container, which can be reached by walljumping up the way to the pipe which doesn't spawn enemies, then entering it. The shutter at the end of the room can only be passed from the left side until you get the wave beam, i. e. you can't return to Upper Brinstar using that passage for now. Open the shutter by shooting the blue button.
As soon as you're in the next room, you'll encounter a disintegrating bridge. Some players get stuck here, because they are unfamiliar with the run button. Press and hold 
while crossing the bridge to reach the other side. By walking through the next gate, you will enter Lower Brinstar!
Norfair gets a visitor!
The next place to go is Norfair, namely to obtain the Hi-Jump Boots. First, jump off the ledge you are standing on and keep going downwards. As you encounter a couple of rocks with a yellow gate nearby, place some bombs at the ground. As a part of the ground will collapse, place another bomb in the pit. Alternatively, you can shoot the ground as well. Continue going lower and lower until you reach the bottom. The green gate on the left side leads to an energy recharger. Use it if you want, then enter the gate on the right.
You'll instantly have to deal with a spot quite similar to the bridge described above. But this time, you have to jump over a water pit. Simply go to the very left, press and hold , run a few steps and jump as far as you can.
The Spazer hides in the next room, however, you can't gain it until you get the Hi-Jump or by doing a Wall Jump to the top. Keep going forward until you reach the elevator, then use it.
Your journey continues in Norfair.
Second Visit
Hidden Upgrade
Before bashing Kraid, you might want to obtain an upgrade for your beam. So, head left again until you reach the first red-solied room. Leftmost, you can notice a breakable block on the ceiling. Shoot it with your beam and jump up through the hole. At the morph-ball tunnel, break the first block with a bomb as usual. But you have to use your beam on the second one. If you use a bomb, a hole will emerge directly under you, causing you to fall down into the water.
Open the gate, then enter it and get the Spazer.
Operating the Spazer
Utilising the Spazer, you will fire three beams at once. This can be pretty helpful when aiming at enemies, not to mention the ability to kill green Space Pirates using the beam.
Battling Kraid
You'll have to shoot and break certain blocks a lot to reach Kraid, which can sometimes be tricky, so read carefully.
Return to the elevator room. As soon as you're there, shoot the lowermost block in the right wall with a Super Missile. Enter the hole, then jump upon the platform beneath the creepy alien head. Enter the gate behind it.
You'll now arrive in a factory-like room. Shoot the platform's leftmost block and go through the hole. In the lower chamber, set a bomb at the lowest block of the right wall and pass through it. Open the gate and kill the mantis-like aliens in the next room. If you want to save before visiting Kraid (which is actually advisable), go to the right, morph into a ball and roll into the pit. Place a bomb and roll to the right. The Save Station is right behind the gate.
To get to Kraid, hold out for a cracked spot on the floor of the room with the mantis enemies. As you find it, shoot it, go through the hole and the gate. The Space Pirates in the next room can easily be killed by using the beam (thanks to the Spazer). At the end of the room, you will encounter a mini version of Kraid. The best way to beat him is simply using missiles (two should do). The next corridor hides a refiller room, but it's not too hard to find it. Shoot the cealing at the spot without solid blocks above. Recharge, if necessary, and go to the next room to meet Kraid.
The battle itself
Kraid is one of the easiest bosses to beat. The best way to finish him is using Super Missiles, since he can only take four of them. As he hatches out of the ground, shoot his face using your beam. As he opens his mouth, shoot a Super Missile inside. If you run out of ammo, shoot the claws flying around in the room. After hitting him with 4 Super Missiles or 20 Normal Missiles, he will drop into the ground again, and that's it!
After the fight, go to the next room to obtain your new item: the Varia Suit! Its main purpose is to protect you from heat, which will be quite handy in Norfair! Plus, it halves the damage Samus will take.