How were the Dwarves captured by the elves and what happened when they were presented before the elves and kings?

Bilbo and the dwarves are still near starving, though they are happy to be alive. They search for food but they are apprehended by a large group of wood-elves. Bilbo slips away and makes himself invisible but the dwarves are blindfolded and led towards the fort of the Elvenking. Bilbo follows behind them as best he can and when the dwarves are made prisoners by the suspicious king, Bilbo realizes that he must do something. The dwarves have separate cells and they are able to eat but Bilbo is still alone, invisible and hungry. He learns a bit about the region by sneaking in and out with differing cargo but as much as he wants to get a message to Gandalf, he knows he will have to save the group on his own. Bilbo visits Thorin and raises his spirits‹of course, Thorin is shocked to hear Bilbo's voice. Bilbo is able to send messages from Thorin to the other dwarves and they agree not to mention their original mission to the Elvenking, as he will want a hefty share of the treasure.

During a night of festivity, Bilbo saves his group by stealing the keys of the drunk jailer, unlocking the cells of the dwarves and helping them fit in a flotilla of empty wine barrels that are being floated downstream. Bilbo has some difficulties but he manages to stay afloat, clinging to the side of a barrel. In the meantime, he hopes that his friends are not drowning in their heavy casks. But at least they are out of the castle-fort and will soon drift onto the banks of Lake-Town.

nope