How does Bilbo rescue the dwarves?

The group is separated and lost. It seems to be some magic at work. Bilbo is alone in the dark and after trying to find his friends, he gives up and goes to sleep. He is arrested in his sleep, attacked by a giant spider that was trying to poison him. Bilbo kills it with his sword and then he, himself, falls down and passes out. When he wakes up he finds his friends swaddled in spider net, suspended from tree branches and guarded by a troop of spiders. Bilbo's invisibility and sword help to get some of the dwarves free.