They escape in barrels sent downriver to be filled.
Bilbo put the dwarves in barrels, and the elves float them down the river with out noticing.
the dwarves were captured by thorn and the wood elves long enough for bilbo to help them escape
The dwarves were captured and imprisoned by the elves in Mirkwood. Bilbo had to keep entering to form a plan and carry it out.
The dwarves realise that it is the only way to escape, and the only chance they'll get to do it.
They were imprisoned at the time he revealed the ring to them. Considering Bilbo used the ring to to go invisible and help them escape, it is likely that the Dwarves were grateful. Although they clearly disliked the actual method of escape (hiding in barrels which were tossed in a freezing cold river).
Bard demands a share of the treasure to help the people of Lake-town. The dwarves offer Bard a portion of the treasure, and the elves offer to help the dwarves in their quest. Ultimately, they all come to an agreement to share the treasure before a battle breaks out.
He uses the ring many times in The Hobbit. He uses it to escape from Gollum and exit the mountain, he uses it when spying on the giant spiders in Mirkwood, he uses it when the Dwarves are captured by the wood elves, and he uses it when in Smaug's lair.
Bilbo snuck out of the Dwarves camp and delivered the Arkenstone to Bard.
I think Gandalf came to Bilbo to either get a 14 man. (Another reply) Gandalf was helping the dwarves, and he believed that Bilbo could help. However, his help to the dwarves was secondary to his main mission: to get information about Sauron. Sauron is mentioned in the Hobbit, as the Necromancer; in the Lord of the Rings, Gandalf confirms that the "Necromancer" was no other than the old enemy, Sauron.
In the book "The Hobbit" by Tolkien, Bilbo doesn't find the dwarfs, the dwarfs find him! (With the help of the wizard) It is a wonderful book and I strongly recommend reading it!
Bilbo's job on the adventure was to act as the burglar, using his stealth and hobbit-like abilities to help the dwarves on their quest to reclaim their kingdom and treasure from the dragon Smaug.
Biblo 'borrows' the Arkenstone.
After Bilbo puts on the Ring and turns invisible, Gollum cannot find him, and thinks he has made his way towards the exit. Gollum heads to the exit and Bilbo follows him.