If there's one thing you're definitely gonna need to do to complete the game, it's collect all 12 of the Chozo Artifacts, the pieces of the Cipher that holds the great evil from spreading the evil throughout the rest of Tallon IV, and consequently, the Space Pirates out of the Phazon core. The only way to kill the Phazon problem altogether is to irradicate the source - Metroid Prime, and to do that, you need to open the gateway at the Artifact temple by using the cipher (and destroy whatever Space Pirate comes after you once you do. *wink*)

So, without further delay, onto the Artifact Location information part of this guide. Artifacts are organised by their numeration in the game (ex: This is the Artifact of Elder, the Third of twelve), and include the hint given to by scanning the totems at the Artifact site, plus the instructions to obtaining the artifact.

#2: The Artifact of Strength - Warrior Shrine (Magmoor Caverns)
"The heat of Magmoor was a test for many warriors. A 'Shrine' in their honor holds the Artifact of Strength."
In the Magmoor Caverns "Monitor Station", where the Pirates have installed a control tower atop an island in the middle of a pool of lava (you'll remember this area, it's on the way to the first entrance into Phendrana Drifts, the first thing you're greeted by upon entry is AD Turret fire and later in the game, Flying Pirates.) On your way out to the door to the access tunnel to the Drifts Elelevator, there is a small platform above the walkway. Once you have the Space Jump and Boost Ball, double jump your way to the top of the Pirate tower, and use the Spinner device to raise a platform that will take you to a ledge on the outer wall of the chamber. Follow the ledge up to a door - inside the "Warrior Shrine" will be a classic sight and one of my favorites of the game. A Chozo Statue with the Artifact in it's hands.
 

#3: The Artifact of Elder - Control Tower (Phendrana Drifts)
"Invaders have claimed Phendrana as their own. A 'Tower' sits atop their fortress. Collapse it to reveal the chamber where the Artifact of Elder is held."
Although the Nintendo Power players guide states that you can do this at any time, I've found that (in at least my copy of the game) this artifact can only be collected after collecting the Plasma beam. In the Phendrana Drifts Research lab, where you first encountered the Flying Pirates, one of the tops of the towers will have a couple crates and a frozen over window on the right hand side once you go in, blow up the crates and use the Plasma beam to melt the window. Look out the window, and you'll see some fuel tanks lined up next to a tower thatis high up in the background. Blow those tanks open and go back out to where the tower crashed. Roll into a ball and into the crack to find the Artifact. Getting out's tricky, just get up into the crashed tower and roll your way to safety.
 

#4: The Artifact of Wild - Sunchamber (Chozo Ruins)
"A 'Sunchamber' high atop our ruined home became the nest of a great beast, and a source of corruption. Many Chozo spirits have been drawn to this tainted place. Release their bond to the world to claim the Artifact of Wild."
After defeating Thardus and collecting the Spider Ball, you can unlock the Magnetic track path that will take you back up into the Sunchamber where you fought Flaaghra. Where the great beast dwelled will now be home to a few Chozo Ghosts. Lock onto them when they're visible and pound them with Charged Power Beam shots and Super Missles. Once they're gone, the Artifact will appear on the dead plant base that Flaaghra left behind.
 

#5: The Artifact of Lifegiver - Sun Tower (Chozo Ruins)
"There is a tower within the Ruins where 'Light' always shines. Move through the waters there to find the Artifact of Lifegiver."
In the room where you got the Morph Ball, there are spiderball tracks on the ceiling. Once you have the Gravity Suit, use the halfpipe formation to boost up to the left hand side (standing where the Morph Ball was located, looking at the entrance to the room), ride the track across the ceiling to the door. Through the passageway, you'll come to a room called the "Tower of Light". If you've already collected the Wavebuster, you'll know this area, but if you haven't, and have over 60 missles on hand, the Wavebuster is located at the very top of this room. To get the artifact, drop into the water, go through a tunnel and jump up on top of a ledge to a door. Behind the door is the Artifact.
 

#6: The Artifact of Warrior - Elite Research (Phazon Mines)
"A room of 'Research' lies within the mines. A corrupted invader is trapped there. Defeat this creature to claim the Artifact of Warrior."
As you make your way through the Space Pirate base above the Phazon Mines, you'll pass through a room called "Elite Research". Where a strange looking stasis tube containing a really big space pirate sits at the center of the bottom of the room. A quick scan of the base of the tube will reveal that it contains Bendezium, a substance vulnerable to a Power Bomb blast. Once you've collected the Power Bomb (and gotten your health and missles back up to a good level), blast the tube open with a Power Bomb and prepare for some fighting. You'll face off against the Phazon Elite, a highly Phazon charged Elite Pirate that is very tough, but doesn't have a missle launcher. Just double jump the wave quakes, avoid firing at the energy siphon, and pummel it's head with Super Missles. If you feel like adding some style, finish the job with the Wavebuster. Once it's dead, the Artifact will appear.
 

#7: The Artifact of Chozo - Life Grove (Tallon Overworld)
"In one of Tallon's far corners, a 'Grove' of life lies. Reveal the pillar beneath the waves to find the Artifact of Chozo."
You'll need the Power bomb (Phazon mines) to collect this one. Out in the area behind the Frigate Crash site, where you exit from the Chozo ruins via elevator and encounter a pair of seedlings and massive bloodflowers, on the other side is a spiraled magnetic track that will take you up to a door at the top of the room. Behind the door is what looks like a dead end. However, a quick scan will reveal a boulder with traces of Bendezium. Use a power bomb to blow up the boulder and roll into the hole and through the access tunnel. (Note: this access tunnel has what looks like a double half pipe (full pipe?), if you want to, you can take the time to roll up to the very top of the upper half pipe, sit dead center, and detonate a normal bomb, you will reveal a hole, fall through it and collect a Missle expansion.). Once you reach the other side of the tunnel, you'll fall into what looks like an inexcapable room, with the X-Ray visor in the center. Collect the X-Ray visor, and turn it on to reveal that some of the walls aren't there. Blast them open with the Power Bomb, and you'll find a very lush area of life (minus the creatures) called the "Life Grove". In the middle of this newly discovered room, lies a small lake, jump in, get into a ball and roll over to what looks to be a cap in the center of the lake, bomb it. You will reveal a platform with a spinner device at it's base, use it to move the bridge to connect the platform to where the Artifact rests.
Getting out of this room however isn't as easy as walking out a door. You'll need to make your way up the side wall via a few platforms and a morph ball path on the wall, and eventually you'll encounter some Chozo Ghosts, looking for their artifact. They're easier to fight now, stay on the platform you're on, switch to X-Ray mode. You can now track the Ghosts 100% of the time and eliminate them at your leisure. Just remember that you still have to avoid their attacks. Once they're defeated, the way out will reveal itself.
 

#8: The Artifact of Nature - Lava Lake (Magmoor Caverns)
"A molten 'Lake' lies within the tunnels of Magmoor. Shatter the column at the lakes center to reveal the Artifact of Nature."
This is an easy artifact to collect. In one of the first rooms you encountered in Magmoor, "Lava Lake" a large pillar of rock sits in the middle. A scan with the X-Ray visor will reveal there really is no middle and an Artifact sits at the center. Blow it open with a Super Missle to reveal the Artifact.
 

#9: The Artifact of Sun - Chozo Ice Temple (Phendrana Drifts)
"Near Phendrana's shores, a 'Temple' stands. Thaw the frozen waters flowing from the Elder to find the Artifact of Sun."
This isn't a hard one to find either. Back when you fought the Sheegoths in the Drifts, on the way to the Chapel of the Elders, you passed through a room called "Chozo Ice Temple". In there, you saw a large Chozo statue on the wall with a stream of ice coming from the mouth, overtop of a basin. Once you have the Plasma Beam, melt the ice coming from the mouth and in the hands by shooting it. Doing so will reveal the Hands are waiting for something. Jump up into the hands and into a Morph Ball, doing so will activate the doorway underneath the basin, which will lead to the chamber where the Artifact sits.
 

#10: The Artifact of World - Hall of Elders (Chozo Ruins)
"Within the ruins of our home we honor our fallen Elders in a great 'Hall'. A chamber beneath the statue holds the Artifact of World."
In the "Hall of Elders" in the Chozo Ruins, when you were in this room before, you killed off Chozo Ghosts and sat Morph Balled in the hands of the Chozo Statue. Through all the Puzzles in the room, there is a wall with 3 Morph ball slots, each covered by an energy shield colour coded for one type of weapon. You should have done the Wave and Ice slots, but once you've collected the Plasma beam, you can complete this Puzzle, and reveal that a door sits underneath the Chozo Statue at the center of the room. Inside the room below, sits the Artifact of World.
 

#11: The Artifact of Spirit - Phendrana's Edge (Phendrana Drifts)
"A tall cave stands at Phendrana's 'Edge'. Seek the unseen entrance at it's top to find the Artifact of Spirit."
This is a fun one to get, calling this the Artifact of 'Spirit' is probably a good choice... When you have the Power Bomb, Grapple beam and Plasma beam, head for the far reaches of Phendrana Drifts, where you'll find a tall tall chamber called "Phendrana's Edge". By alot of platform jumping and several instances of Grapple beam endeavors, scale your way to the top of the chamber, to where a bare rock wall is located. An X-Ray scan of the wall will reveal a door behind it. Detonate a power bomb and go through the Plasma door to the Artifact resting place.
If you want to, you can continue up to the top, where you'll find a morph ball hole that will lead you to a Power Bomb expansion.
 

#12: The Artifact of Newborn - Phazon Mining Tunnel (Phazon Mines)
"Invaders mine the depths in their greed. Forge a path through a 'Tunnel' of the Great Poison to claim the Artifact of Newborn."
On the way through the Metroid Quarantine and Fungal Hall areas on the lowest level of the Phazon Mines, heading towards the Elite Quarters where the Omega Pirate was located, you passed by a few blocks in the "Phazon Mining Tunnel" that could've been blown up with plain bombs but they lead into Phazon infested ground. After defeating the Omega Pirate, you have the Phazon Suit and you're no longer affected by the damaging radioactive effects of raw Phazon. Now you can go back in through those passageways and find the Artifact of Newborn, the Last of Twelve.