Several folks have already broken down Acererak's riddle. I'm going to break down the Tomb. The following is the quickest, safest walkthrough for the Tomb of Horrors:
First, locate the true entrance to the Tomb. Avoid the two false entrances. All three entrances are hidden behind loose earth on the north side of the burial mound. You'll need to dig to find any of them. The true entrance is between the two false entrances, roughly in the center of the hillside.
The true entrance leads to Area 3, a long, wide corridor. Follow the corridor to the south. There are 5 pit traps in the hallway, but it is possible to avoid crossing them. Note that the red path in Area 3 crosses 3 of the 5 pit traps. Ignore Area 4; it is a pit trap.
Study the red path if you want to learn Acererak's riddle. The clues it provides are in brackets below.
Ignore Area 6, the Face of the Great Green Devil [Shun green if you can,]. It is a lethal trap.
Approach Area 5, the Arch of Mist [Go back to the tormentor or through the arch]. Poke the glowing stones around the edge of Area 5 in the correct order -- Yellow, Blue, Orange. When the mist clears, walk through the arch while standing on the red path. Failure to follow the proper procedure is not immediately lethal, but teleports you either to Area 7 or Area 3.
Arrive in the Area 10, the Great Hall of Spheres [and the second great hall you'll discover]. Ignore Area 10a, the misty arch at the end of the hall, it is a (non-lethal but sucky) trap.
Follow the crawl space behind the Red Sphere. Follow it to the secret door and continue to Area 13, the Chamber of Three Chests. The PC taking point will automaticall fall and take 1d6 points of damage. Inside Area 13, open the Silver Chest. Be aware that it contains a non-lethal dart trap. Take the Ring of Protection+1 and return to Area 10 [If shades of red stand for blood the wise will not need sacrifice aught but a loop of magical metal]. Ignore the other two chests. They are trapped and start dangerous combats.
Back in Area 10, follow the crawlspace behind the Black Sphere [night's good color is for those of great valor.] Find the secret door. You have a 1 in 6 chance. If you cannot find the secret door yourself, you need to get the Gem of Seeing from Area 11. That gem is the only magical way to find the secret door.
Assuming you found the secret door, enter Area 14, the Chapel of Evil. Take the treasure from the first three rows of pews. Do not open the row of pews closest to the altar, it is a non-lethal, strength draining trap. Do not touch the Opalescent Blue Altar, it is a damage dealing trap. Do not enter the Archway of Glowing Orange, it is a gender bending, alignment swappig trap. Carefully inspect the southeast corner of the Chapel. You have a 4 in 6 chance of finding the way forward.
The way forward is Area 15, the Stone Gate. Stick the Ring of Protection+1 from Area 13 into the slot [sacrifice aught but a loop of magical metal -- you're well along your march.] A secret door will open. Follow the hallway beyond down the stairs and to the west. You'll find a door with a pit trap behind it; a second door with a pit trap behind it; and a third door with a pit trap behind it. There's a secret door at the bottom of the third pit trap [Two pits along the way will be found to lead to a fortuitous fall, so check the wall].
Open the secret door in the third pit trap. Another secret door is immediately on your left, to the east -- Area 17, the Magical Secret Door. Area 17 can only be found by using a Gem of Seeing, "a similar spell" (presumably True Seeing), or Detect Magic. It can only be opened by casting Disepl Magic or Remove Curse. Find and open it.
Follow the hallway behind Area 17 to Area 19, the Laboratory and Mummy Preparation Room. There are three stone vats in the room. Ignore the first. The middle vat contains half a golden key submerged in deadly acid. Drain the acid out of the vat, or find a way to safely fish out the half-key. The last vat contains the other half of the golden key and a deadly slime. Fight the slime, and recover the second half of the key. This combat is mandatory. Join the two halves together, and you have the FIRST KEY [These keys and those are most important of all].
Beyond Area 19 is Area 20, the Huge Pit Filled With 200 Spikes. If you try walking across Area 20, you'll take some damage. Cast Fly, Levitate, Teleport, Dimension Door, Jump, Spider Climb or just use a rope to get across.
There's a secret door to the north 60 feet past Area 20. Open it to find Area 21, the Agitated Chamber [beware of trembling hands]. Area 21 is the most dangerous room you have to enter in the Tomb. The floor shakes randomly, and the tapestries will turn to green slime if you damage them. The best way through is to say off the floor. Fly to the northwest corner of the room, carefully move aside the tapestry (possibly using Telekinesis), and find the secret door on the other side.
Follow the hallway east beyond Area 21. Avoid the pit trap in the intersection and go north. Open the false door and find the secret door on the other side [If you find the false, you'll find the true]. Go through the secret door and immediately look down. There is a secret trapdoor set in the floor. Open the secret trapdoor and go down. Do NOT continue north or you will encounter another lethal trap (the Juggernaut).
Continue along until you find Area 24, the Adamantite Door. Shove three swords into the slots in the door and enter Area 25, the Pillared Room [into the columned hall you'll come].
Do not touch the pillars in Area 25 they are a potentially dangerous trap. Ignore the doors to the north and the gem in the southeast corner. Proceed directly to throne set against the southern wall [there is the throne that's key and keyed]. Take the golden crown but do not try to wear it. Touch the silver end of the scepter to the silver crown inlaid on the base of the throne. This will open the way forward.
Proceed to Area 28, the Wondrous Foyer. Pick up the SECOND KEY [These keys and those are most important of all]. Keep in the mind that the SECOND KEY is protected by an Antipathy spell, so picking it up might be a challenge. Area 28 leads directly to Area 29, the Valves of Mithril. Open them by placing the gold end of the scepter into the depression between the two doors. Trying to use either key in the Valves of Mithril will cause damage. Using the wrong end of the scepter will automatically kill you.
Follow the doors to Area 30, the False Treasure Room. Carefully open the bronze urn to obtain the services of an Efreet. Move the statue to the northeast. Doing this requires three people who each have a least a 16 strength. You might need the Efreet's help.
Follow the hallway to the west until it turns north. There is a secret door to the south. Open the secret door with the FIRST KEY and enter Area 33, the Crypt of Acererak the Demilich.
The room looks empty, but there is a small keyhole in the floor. Move the whole party as far north as possible. Have the fastest moving PC put the SECOND in the keyhole and turn it to the right 3 times. (Note that using the FIRST KEY will cause a damaging explosion). As soon as you finish turning the key, run north. Otherwise, you will be squased to jelly as the floor rises up to the ceiling.
Enter the vault and take everything that isn't (a) nailed down or (b) a jewled skull. Ignore the ghostly creature that appears to threaten you, it's harmless. Ask the Efreet to put the Gold Crown from Area 25 onto the skull and to touch the crown with the silver end of the scepter from Area 25. Tell the DM that Gygax himself approved of this course of action, and laugh as Acererak is turned to fetid powder.
Return to town. Buy Ale and Whores.
Note that there is only one mandatory combat in the Tomb (the slime in Area 19) and only two one unavoidable death traps (Area 21, the Agitated Chamber, and the risk of being killed trying to open Area 29.). There are also nine covered pit traps to bypass, each of which is potentially fatal.
i]Edit: Upon review, I decided Area 29 is not a mandatory deathtrap[/i]