Amongst the stash of treasure and weapons taken from poor dwarves, elves, orcs and men captured and eaten by these trolls is a tiny elvish blade, barely bigger than a dagger for a regular man, but just the right size for a Hobbit.
Unless I’m misremembering Fellowship, Peter Jackson filmed Gandalf handing Sting over to Bilbo to mirror Bilbo giving Frodo the sword in LOTR. In other words, he makes a moment out of it. With the beautiful green forest in the background (cave entrance), Martin reluctantly receives the sword, pulling it slowly out of its sheath.
Thorin gets Orcrist here as well, which you can see him wield in his promo picture by the way. Orcrist is a long, flat blade and they filmed a scene of Richard Armitage swinging it down in a wide arc striking down a leaping evil thing to be added in digitally before all is said and done.