To enter the Astral plane, you need to look at the tapestry at Geary's, in Shadow Square. Talk to the half-giant, and, if he's in a good mood, he'll tell you about some strange dreams he did about that tapestry. Then go close to the tapestry and look at it again, you'll find yourself teleportated in a very strange place...
You will find some very strange creatures named the Psurlons, as well as a very mysterious Rybochka. Talk to Garzak the Psurlon leader, and he will ask you to do some quest for him in order to free Athas, that you will be richly rewarded for that task, etc... You will have to find and bring back a tapestry that seems to have some unusual powers, according to the Psurlon leader. Don't forget to beg for a magic flute otherwise you'll never be able to go back in Astral. You can also look at the frame in southern part of area, you'll notice that it's probably the place for the tapestry to hang.
You will find the tapestry in the guard room in Altaruk. When you pick it, you think to yourself that it might really need some repairs. Of course, your perfect knowledge of Athas will lead you to Sinifa's shop in Caravan Way, who will fix it for only 20.000 CPs. She also suggests that you can talk to Pa in the fields. The very knowledgeable Pa tolds you that you must find some place to hang the tapestry, and that it will allow you to travel through planes.
Go
back to the Psurlons using the flute as you are close to the tapestry at
Geary's. Give the tapestry to Garzak, and instead of giving you a reward,
he says that he also needs a crystal. Unfortunately, the naughty humans
have broken that crystal in 3 parts and buried the shards in some places
around Tyr. But you can recover them using the powers of the flute, as
the shards will show off if you blow into the flute while near one of them.
The shards are not very difficult to find, just go in Oasis (Elven Caravan), 3 sands (Nomad Camp) and Defiled desert and use the flute, then go where you "saw" the shards and dig (you need a shovel), till you find each shard. Note that the shards don't appear in inventory.
I'm unsure of what to do then. If you go to Astral and give the crystal to Garzak, he will kick you out of Astral plane without the slightiest reward (he will even have gotten the flute back). And if you don't give the shards and say he'll taste your blade, he kicks you out in the same way. I also tried to look at the tapestry that now hangs in Astral plane but nothing occurs...