Upon first entering the hut you'll see Ernest. Talk to him about what he's doing out there, and make sure to ask him what he used to do his research. It costs 250 coins to use one of his teleporters.
Once you've talked to Ernest and bought your teleporter ticket head into the next room. There's a door leading to the north. If you go through this door you can steal a few items for selling.
Now walk along the bookshelf until you get a message about a book. Taking the book results in Ernest sending you to the Drake Cave the first time you use one of his teleporters, but after that you can use the teleporters normally.
The book is important for two reasons. First, it teaches you Dispel Barrier Lv.3. I've heard that you can also learn the spell in Squiggus, but I've never found it there. You'll also get a quest to steal the book from someone in Golddale, and your reward for that quest is a couple points in the special skill Resistance, but it also knocks your repuation down a little bit. Since that's the only way to get that skill I consider it worth it.
The door leading to the east is the room with the teleporters. Starting in the southeast corner and going counter clockwise, the portals lead to Krizsan, Shayder, Sharimik, Lorelei and Gale. If you've stolen the book it doesn't matter which one you go through, you'll still be teleported to the Drake Cave.