Arcanum has a long and a somewhat convoluted campaign, and the game isn't always good about telling you what you should be doing. In fact, the only way to see what main quest you're working on is to check the screenshot on the load game screen. So if you're not sure what you should be doing, here is a walkthrough in brief.
1. Go to Shrouded Hills and ask Ristezze about the ring you got from the gnome Preston Radcliffe. After making a trade, he'll tell you it was made by P. Schuyler & Sons in Tarant.
2. Go to Tarant and talk to or kill the Schuylers. You'll learn they made the ring for Gilbert Bates.
3. Talk to Gilbert Bates (still in Tarant). He'll tell you that the gnome was really a dwarf named Stennar Rock Cutter, and that his clan, the Black Mountain Clan, disappeared some time ago. He'll then ask you to look into the matter.
4. Go to the home of the Black Mountain Clan and talk to Gudmund Ore Bender. He'll tell you that the Black Mountain Clan was exiled to the Isle of Despair.
5. Go to Edward Teach in Ashbury and have him sail you to the Isle of Despair.
6. On the Isle of Despair, learn that the Black Mountain Clan was never there.
7. Go to the home of the Wheel Clan and find Loghaire, the king of the dwarves. He'll tell you that elves were behind the exile of the Black Mountain Clan, and he'll tell you the name of one of the elves involved: M'in Gorad.
8. Go to Stillwater to learn the location of the elven city of Qintarra.
9. Go to Qintarra to learn that M'in Gorad is the name of a dark elf.
10. Go to the Hall of Records in Tarant to learn about Renford A. Terwilliger, who purportedly visited the dark elven city of T'sen-Ang.
11. Still in Tarant, visit the library to ask about Terwilliger's book. Accept a book about Terwilliger's book instead, and learn that the last remaining copy of Terwilliger's book belongs to Victor Misk in Caladon.
12. Go to Caladon to get the book but learn it isn't there.
13. Go to Roseborough to get the book.
14. Go to T'sen-Ang.
For good-aligned players...
15a. In T'sen-Ang, learn from M'in Gorad that the Black Mountain Clan was exiled to the Void to help bring about the return of Arronax.
15b. Go to Qintarra to learn that your quest involves Nasrudin, who banished Arronax to the Void.
15c. Go to the First Panarii Temple in Caladon to learn that Nasrudin isn't buried there and might in fact be in Thanatos.
15d. Complete a quest to purchase a ship, and sail to Thanatos.
15e. Meet with Nasrudin to learn you need to find the Vendigroth Device.
15f. Go to Tulla to learn the location of the Vendigroth Ruins.
15g. Explore the Vendigroth Ruins to find the Vendigroth Device.
15h. Meet with Nasrudin at the Ring of Brodgar in Roseborough to be banished to the Void.
For evil-aligned players...
15a. Butcher everybody in Stillwater to gain the trust of M'in Gorad.
15b. Learn from M'in Gorad that the Black Mountain Clan was exiled to the Void to help bring about the return of Arronax.
15c. Go to the First Panarii Temple in Caladon to meet up with the high priest H'an Kua and accept an assignment to find the Vendigroth Device.
15d. Go to the Dark Elf Camp in the Vendigroth Wastes to discover the location of the Vendigroth Ruins.
15e. Explore the Vendigroth Ruins to find the Vendigroth Device.
15f. Meet with K'an Hua at the Ring of Brodgar in Roseborough to be banished to the Void.
16. In the Void, meet up with Arronax to learn he has nothing to do with what's been going on.
17. Defeat Kerghan to end the threat.