Unfortunately there is no legitimate way to return to the Isle of Despair once you've left, however there is a glitch that can allow one to return...
1 - Gate Guard Edit
The gate guard won't know anything about the Black Mountain Clan, but he will tell you a couple things: that the enclave (where you are now) is run by Thorvald Two Stones, and that Thorvald has a bodyguard named Ogdin.
When you break off the conversation, the guard might also tell you that it's dangerous to wander around outside the enclave. It seems a magical beast has been prowling around the area. You can find the beast by first crossing the land bridge (#2) to get to the other side of the moat, and then following the tracks (#3) to the north.
Eventually the tracks will lead you to a ruined building and a "temporal crusher." The crusher can freeze enemies for a short period of time, but as long as you have some companions with you it shouldn't present much of a problem. Once it's dead, you can find a junk pile inside the building. The junk pile always contains baneful gauntlets (hexed) and a charmed ring.
When you return to the gate guard to tell him the good news, you'll receive 1200 experience, a serpentine necklace, and a small boost to your alignment. You'll get the reward whether the guard told you about the beast (and triggered the quest) or not.
2 - Land Bridge Edit
The bridge allows you to cross the moat.
3 - Tracks Edit
If you follow the tracks north you'll find the lair of a temporal crusher (see #1). If you head east from the tracks you'll run into a trail leading north. At the end of the trail, hidden behind some foliage next to a tree, you'll find a chest with 1837 gold in it.
4 - Cynthia Boggs Edit
She'll tell you that she was born on the island, and that she has been "abused and treated like common property" since her mother died. Not surprisingly, she'll ask you to help her, and she'll tell you about a tribe of nomadic women who live on the island. Then she'll mark the location of their camp on your world map, and, if you're male, she'll give you a white scarf to wear so the women in the tribe will know you come in peace.
However, when you visit the tribe and speak with its leader, Lorria, she'll tell you that they don't want Cynthia in their tribe if she can't make it to them on her own. Then she'll give you an old revolver to give to Cynthia to aid her in her escape.
When you return to the enclave, Cynthia will be perfectly willing to take the revolver and try to escape on her own, but she doesn't have any skill with firearms, and so she'll just get herself killed. If you decide to help her further, she'll join your party, and you'll have to sneak her to the women's camp. Either way, you'll receive 1500 experience and a boost to your alignment when you talk to her.
There are a couple ways to get Cynthia out of the enclave. If you're persuasive, then when a guard stops you and tells you Cynthia isn't allowed to leave, you can tell him that you own her, and he'll let you pass. If you're feeling violent, you can simply kill all the guards who try to stop you (this doesn't seem to prevent you from completing any quests). Lastly, if you're feeling sneaky, you can unlock one of the windows in the outer wall, and then lead Cynthia through the window after she starts following you.
When you get Cynthia to the women's camp and speak with Lorria again, Lorria will allow Cynthia to stay. Cynthia will stop following you, and, if you demanded payment when you first talked to her, she'll give you her locket (which isn't useful for anything). You won't get any more experience.
As an alternative, you can also take Cynthia with you when you return to Ashbury. This is possibly the best solution for her, and you might even get a fate point for it. (I've heard people say you get one, but I've never gotten one myself. If you know exactly how to get the fate point, please let us know.)
5 - Norian's House Edit
Norian brews potato moonshine, and he'll ask you to deliver a jug of it to Maximillian, who lives north of the enclave (he'll mark the location on your world map). When you reach Maximillian, it's easy enough to give him the moonshine and get a receipt for it, but you should also talk to him. He'll be reluctant to speak with you, but if you take the dialogue option starting with "Every man has his secrets...." then he'll open up and tell you about himself.
You'll learn about the downfall of Cumbria (which should be familiar if you've been to Dernholm and Black Root), and you'll learn that Maximillian is really King Praetor's older brother, and thus the real heir to the throne. You'll automatically convince him to return to Cumbria, and he'll ask you to find a man named Warren Pel Dar, the captain of the Dragon Knights, and tell him that Maximillian is on the Isle of Despair. If you've already met Warren's daughter Lianna Pel Dar in Dernholm, then you'll be able to tell Maximillian that Warren is dead, but that Lianna is a fighter like her father was, and Maximillian will change the quest and have you notify Lianna instead.
When you return to Norian you'll receive 1200 experience and a jug of Norian's potato moonshine. Later, when you speak with Lianna Pel Dar, she'll decide to bring the rightful king back to Cumbria, and you'll receive 1500 experience and some alignment.
6 - Jones the Collector's Shop Edit
Jones will ask you to go to Shades Beach and pick up some unspecified objects for him. He'll also mark the beach on your world map. When you get there, you'll find a large ruined contraption (it's a submarine) guarded by several spiders and a skullcrusher. You should also find some technological items littered around the contraption: two schematics (one for Bronwyck's Gun and one for Reanimator), an ancient pocket watch, an ancient filament, ancient gears, and an ancient looking glass.
When you return to Jones, he'll accept the gears, looking glass, or pocket watch, and you'll receive 1500 experience plus an ancient gun chassis. The chassis is a component of Bronwyck's Gun.
7 - The Pit Edit
8 - Gorrin, Master of the Pit Edit
Gorrin schedules fights in the pit. To get in to see Thorvald, you might have to win at least one such fight. However, to take part in the fights, you'll have to tell all of your companions to wait, and then do the fighting by yourself. So save your game first, tell your followers to wait, and then make sure you can get them all to re-join before continuing.
There are five possible battles in the pit:
a) Borag, a level 10 half-ogre
b) A level 12 human bandit
c) A level 11 elven thief (carrying a dagger of speed)
d) A level 14 human bandit (carrying a special 10-15 damage sword)
e) Three level 15 halflings
If you're quick you can loot their corpses before being teleported out of the pit at the end of the battle. Once you win all five battles, you'll gain the reputation "Champion of the Pit."
9 - Ogdin Edit
Ogdin is blocking the door to Thorvald's house, and you'll have to convince him to let you pass. The sure-fire way to do this is to prove yourself in the pit by winning a battle there (see #8). The easier way is if your character notices that Ogdin doesn't seem to approve of the pit fights. Then if you have a copy of The Hand with you (found at the Ashbury docks), he'll decide that you're a decent sort and let you pass. You'll also earn 800 experience. Finally, as a last resort, you can kill Ogdin (and then Thorvald) to get the information you need.
You can also tell Ogin that he seems very articulate for an ogre, and he'll tell you some of his background. This information is related to the Matt de Cesare quest in Tarant.
10 - Thorvald Two Stones Edit
The main reason for coming to the Isle of Despair is to ask Thorvald about the Black Mountain Clan. However, he'll claim he's the only dwarf on the island, and he'll be disturbed to hear that his clan (the Wheel Clan) was the one behind the supposed banishment. Finally, Thorvald will tell you that the Wheel Clan hides the entrance to its home, and that the only way to detect it is to wear special glasses made out of kathorn crystals. He'll mark the location of the Wheel Clan on your world map.
From here you'll have a few options. If you have enough persuasion, you can ask Thorvald to join your party and then get the glasses from his inventory (ask him if he's a dwarf or a gnome). If you're intelligent enough, you can convince Thorvald to give you his glasses (tell him he can claim they were stolen, and then agree to tell the Wheel Clan of his plight). You can also kill Thorvald and then read his diary and get the glasses off his corpse. Or you can steal a schematic for the glasses from the chest next to Thorvald's bed. Finally, you can go to the spectacles shop in Ashbury and ask the proprietor there to make you a pair. But note: the last two options require you to have a pair of kathorn crystals. If you've already explored a lot of Arcanum, and you didn't save any crystals, then you should probably get the glasses from Thorvald one way or the other. Once you leave the isle you can't come back, so it's better to be safe than sorry.
A. Exit to the world map and Edward Teach's ship. Once you leave the island you won't be able to come back, so make sure you have or can make the special Wheel Clan glasses before you leave.