Here are what all the clues mean with room/area references.
It should be noted that the Tomb of Horrors is a very linear dungeon and the clues are generally arranged in the order that a party progressing through the dungeon will reach them. Some clues have been frequently misinterpreted by fans of the module, so I'll try to explain how the common misinterpretations that I have encountered are wrong.
Go back to the tormentor or through the arch,
And the second great hall you’ll discover.
This clue means that moving through the arch at 5 (after pressing stones in the proper sequence) or the concealed door behind the painting of the tormentor at 4 will lead you (eventually) to area 10, which is identical in dimension to the entry hall (area 3) and similarly decorated (i.e., a second great hall).
Shun green if you can...
Shun green means avoid the green devil sphere of annihilation trap at 6, and the similar devils in area 25. The "if you can" implicitly includes the devils in 25 because characters who touch the columns in that area and become weightless will be blown by an air current toward the devils in 25 and may not be able to avoid them. Avoiding the devil at area 6 is easy, you just stay away from it.
Common misinterpretations: This clue does not refer to the green sphere in 10, which is harmless and doesn't need to be "shunned." Further, the cover art of the original module depicts green-colored columns, which suggests that this may also be a reference to the columns in 25, which are harmful if touched... but the description of 25 states that the columns (all of which are harmful) are all different colors. Further, the encounter on the cover art appears to be the one that occurs in 18A (even though there are no columns in that room). So I do not believe this refers to the columns in area 25. Finally, in a meta sense some have joked that “shun green” is warning players to stay away from the module altogether (the module’s second 1e cover was green). This, of course, is tongue in cheek since the original cover was not green and the module was played at the Origins 1975 Convention, three years before even being published.
but night’s good color
Is for those of great valor.
Night's good color is the black sphere in area 10 which leads further into the tomb toward Acerarak (meaning you need valor to go there).
If shades of red stand for blood...
This refers to the red sphere in area 10 which leads to a dead end containing strength-sapping combats that don't further the quest (bleeding the party).
...the wise Will not need sacrifice aught but a loop of
Magical metal—you’re well along your march.
This refers to area 15 where the party will find a small slot in the wall. By dropping a magic ring through the slot (permanently losing it), the party will open this section of wall to a passage that is necessary to continue. By this point the characters are roughly halfway through the dungeon, so "well along their march."
Two pits along the way will be found to lead
To a fortuitous fall, so check the wall.
The "two" here is is vague. There is one pit (the third one beyond area 15, just north of 17) that has a secret door in its south wall that is essential to reach the end of the dungeon, so that is definitely one of the two. The other could be a reference to the trapped door at 23, though a trapped door isn't exactly a pit and there is no secret door at the bottom. There is another pit--the southernmost one in area 3--that has a secret door in its wall, but this is one-way and only leads in to the pit, so if you fell into the pit, you would not be able to find the secret door by checking the wall. My best answer here is definitely the pit beyond 15 and just north of 17, and possibly the trapped door at 23. When I run the adventure, I turn the trapped door at 23 into a pit trap so the riddle makes more sense.
Speculation: It is possible that the original version of the adventure had two pit traps with secret doors leading out of them, and Gygax/TSR forgot to change the poem when they took one out. The pit in area 3 might originally have had a 2-way secret door that you could find and use from inside the pit, instead of a 1-way door leading only into it.
These keys and those are most important of all,
The First Key (area 19) and Second Key (area 28) are required to reveal and enter Acerarak's Tomb, making them most important.
And beware trembling hands...
This is the most vague clue in the poem. My best interpretation is that it refers to room 21, which has a mechanism that jostles the room and could possibly cause players to tear the tapestries there if they are holding them in their hands. Tearing the tapestries turns them into green slime and brown mold. It could also be interpreted by players as the effects of the fear gas at area 18, although nothing in the module explicitly states that the gas causes trembling.
and what will maul...
Weapons are objects that are intended to maul, and the weapons hanging on the walls of room 27 will animate to attack if the party enters the room. I believe this line is a reference to room 27, though it is a bit out of order. You could argue that it also refers to the few physical-attack monsters in the dungeon (areas 8, 13, 18B, 19) or the juggernaut (area 23C) as well, though that would be a rather obvious warning from Acererak, considering his other warnings have much more obscure meanings. If the clue is interpreted to mean the weapons in 27, it could actually help the party avoid the encounter (which is unnecessary to complete the adventure). It would not help them avoid monsters any more than they could avoid monsters anyway, so I think the strongest argument is that the clue refers to the weapons in 27 only.
If you find the false, you’ll find the true
This clue refers to the false door at 23A, which opens on a stone wall that is actually a secret door. First door is false, but the secret door is true and necessary to reach the end.
Common misinterpretation: The clue is often misinterpreted to mean the false tomb at 30, which you must reach to find the real one at 33; however, finding 30 does not necessarily lead to finding 33. You could find 30 and miss 33 entirely. Finding the false door is a final dead end, so players will eventually search that section of wall and discover the secret door. Also, given the generally chronological order of the clues, this one comes at the point where the party reaches 23, not 30. Finally, in the original version of the module, area 23 is actually entitled "FALSE/TRUE DOOR," which I believe is direct evidence that Gygax had 23A in mind when he wrote "find the false, you'll find the true."
And into the columned hall you’ll come,
Area 25 is a huge room with columns beyond the true door at 23.
And there the throne that is key and keyed.
The throne in area 25 is key to reaching the end and it is keyed open by the scepter sitting on it.
The iron men of visage grim do more than
Meets the viewer’s eye.
This refers to the iron statues in area 30. One of them conceals a secret passage that leads to the end of the adventure, area 33.
You’ve left and left and found my tomb
The use of the contraction "you've" might obscure the fact that the first "left" means the verb left, not the direction. Drop the contraction and it is clear: "you have left." The clue means that when the party has left (verb) area 30 into the hall beyond the secret door and they search to their left (direction) they will find the keyhole (to the south as they travel west--left) to enter area 33, Acerarak's tomb.
Common misinterpretation: This clue does not mean take two left hand turns--that interpretation (after making a right turn first) will lead the party away from Area 33 and dump them via a magical one-way door to a point earlier in the dungeon.
And now your soul will die.
This is an explicit reference to the demilich's form of attack, tearing the soul out of intruders in his tomb.
In area 8...
In the gargoyle's collar is a note: "Look low and high for gold to hear a tale untold. The archway at the end and on your way you'll wend. -A" The note refers to the gold sphere in 10, which leads to the encounter in room 11. The archway at the end of area 10 will eject anyone who enters it outside the dungeon entrance naked (all their stuff goes to 33)... so they are "sent on their way." And the A is Acerarak's signature.
In area 11...
If players place gems into three of the four gargoyle statue hands, the hands close and crush them. A magic mouth then says: "Your sacrifice was not in vain, look to the fourth to find your gain." This refers to the other of the four hands, which will then be holding an invisible (at first) gem of seeing.
In area 27A...
The message from Acerarak has no hidden meaning I could discern. It's just taunting.