You'll land straight into the game after watching and reading a short intro narrative of Samus landing on Zebes for her first mission ever. Once Samus appears in Brinstar at the exact same spot she started out at in the original Metroid the remake madness begins. Let's get right into it by traveling left and climbing over the rocky terrain you'll find.
Watch out for the Zoomers crawling around, even with a short beam range they won't be much of a challenge for the famous hunter. Beyond this you'll find your first critical item - the Maru Mari, or Morph Ball as it's affectionately known. Each time you collect a new item the game will give you a brief description of its powers, be sure to read them in full so you won't miss out on anything.
With the Morph Ball in your grasp backtrack to the right and crawl under the rocky structure using the Morph Ball to fit in the narrow space. Backtrack past the entry point and keep going right down the cavernous corridor while blasting Zoomers blocking your path. Head through the blue door at the end and cross through the next chamber, not worrying about the Bomb Blocks in the floor for now.
Further in the next corridor you'll be ambushed by three Skree from the ceiling. Run past them and stay back when they explode to avoid the nasty shrapnel they expel. Crawl under the large outcropping from the ceiling and proceed right to find the first itemless Chozo Statue. Jump onto its empty hands and activate the Morph Ball. The statue will glow and a heavenly tune will begin playing, before the screen displays a map showing you where the Long Beam can be found.
Once you've seen the location clearly, hit A to return to the game. The statue will sit down and release Samus before restoring all of your health and ammo - remember that all the Chozo Statues, including the ones holding items, will restore your health and ammo whenever you activate the Morph Ball whilst standing on their hands.
We'll now go and track down the Long Beam. Enter the new section of corridor behind the statue and cross into the next room. You'll find yourself at the base of a gigantic shaft, save your game in the Save Room beyond the right door ahead before climbing up. Ascend the shaft while taking care to avoid the Zoomers crawling about and avoiding the for now-invincible Ripper flying about.
Climb up past the door on the right wall you'll eventually find to reach a door on the left wall. Enter this new corridor beyond and cross to the end. Shoot open the door there and go inside to find the Long Beam waiting in the hands of another Chozo Statue. With your beam range expanded, go back into the corridor and jump up to the narrow tunnel jammed with blocks just beyond the Skree.
Shoot out all the blocks and jump up through the opening in the ceiling beyond. Climb up the hidden shaft you'll discover to eventually find yourself inside the long corridor north of the Long Beam's corridor (check the map). For now take the left path and make sure not to fall in any of the acid pits. Cross through the door at the left end to find yourself in the Gold Statue room.
Here you'll discover a giant statue carved with both Ridley and Kraid's heads on either side. As you might have guessed this path leads to Tourian but of course you'll need to defeat both monsters before the statue opens up. Go back into the previous corridor and head all the way to the right end. You'll find a sealed door, but then a large and nasty looking Sidehopper will bound down into the room.
Watch its movements carefully (especially on Hard, this thing packs a punch) while ripping into the monster. After taking a beating the thing will eventually blow. Right on cue the door will begin flashing indicating that it's now unlocked. Go inside to find another Chozo Statue blocking the path, but thankfully it's facing you so you can stand on its hands for more directions. This statue will direct you to the Bomb upgrade hidden way over on the eastern side of Brinstar, so we'll take a trip there next.