What methods have been defined to be workable and to be forbidden as far as travel to and from the Dark Sun campaign world goes? Any edition's info will work; I'm running 2e but I can always modify what's out there.
You can (sometimes) get in and out from Sigil.
From The Planeswalker's Handbook, page 32
A secluded, hard-to-reach world called Athas is notable for a couple of reasons. First, "hard-to-reach" isn't just hyperbole; portals leading here are rare in the extreme, and spells that allow interplanar travel fail more than half the time. Recently, the githyanki attempted to reopen one of the few permanent portals to this world from the Astral, but their efforts were thwarted by the natives - which says a good deal for the inhabitants' might. Also, while the priests here have interesting connections with the Inner Planes, they refer to a number of the Paraelemental Planes by different names - so don't be confused if the sods talk about places called the plane of Sun or Rain.
There's also a psionically-powered Planar Gate in the boxed set adventure City by the Silt Sea. This is an artifact.
You can use the World Serpent Inn, initially described in the 1e game accessory, Tales of the Outer Planes, published in 1988. [It is worth noting that despite being a 1e product, it has THAC0 defined in it already, and it is readily usable in 2e.]
The World Serpent Inn is an extraplanar inn with doors that open to pretty much everywhere in the multiverse and going in can be just as easy as entering the inn on one plane for a drink and exiting at another plane. For some more information about it, see this answer.
Specifically for travel to Athas, there is a Dragon #351 (January 2007, 3.5e) article on the World Serpent Inn, which mentions Chch'kraran, a thri-kreen regular of the Inn, who stumbled in by accident and never found a way to return.
More interestingly, the same Dragon issue has another article aptly named "Athas and the World Serpent Inn". It starts as:
Deep in the back hallways of the World Serpent Inn stands a door kept under lock and key for as long as anyone can remember. Sands seeps in around the edges of the door, for the desert world - Athas - burns on the other side, ever under the searing heat of its darkened sun.
And of course it goes on to describe what characters can encounter when they open that door.
It was noted that Athas isn't reachable from the other game worlds during the AD&D 2E run. I don't recall if it was in the Dark Sun boxed set or the Spelljammer materials, or in a late 2E FAQ.
It was implied that this is because it's the far future of the Forgotten Realms, but that particular assertion wasn't explicit.
I don't know if that's still held true with the 4E version.