The main external conflict is between the main characters (Bilbo, the Dwarves, and Gandalf) and the quest to take back the lonely mountain, including all of the things along the way. The group is constantly crossing orcs, giants, elves, goblins, etc. These things that come across the group create constant sources of conflict.
As the group are seeking shelter inside of a mountain that they are attempting to cross, they stumble into a mine of goblins run entirely by The Goblin King himself. The group have to work together in skeptical ways to decieve the goblins and to escape. Whilst the dwarves are busy dismantling and evading goblins, Bilbo finds himself in a secret cavern, only to stumble upon a terrifying multi-personalitied creature, but also a magical ring.
After a long, un-restful journey through the mountains, the group find themselves trapped in a forest full of giant spiders. With almost no hope left, elvish folk finally arrive and rescue the group. This conflict is greatly saturated with fighting not only between the spiders and the elves/Dwarves, but with fighting between the Dwarves and elves verbally.
Bilbo and the Dwarves are seen all evading and running from the great Smaug, a fire breathing, death defying dragon, trying to figure out a way to defeat it. Just when they thought they were dead, Smaug leaves the Lonely Mountain and starts terrorizing a nearby city. A fisherman named Bard shoots down the dragon with a bow and arrow, ending its reign of terror.
The Battle of the Five Armies is a scene in which five different sides faces off in a blood ravaged mountainous area. The towns people and the Elves are attacking Bilbo's crew and the Dwarves from the Iron Hills under the rule of Dáin, who comes once word was spread that Bilbo and company were in trouble. As this battle is occuring, orcs and goblins under the rule of Bolg come and join the fight, hence Gandalf having slain the king goblin back in the caves.
After winning the battle, Bilbo and Gandalf part ways with the Dwarves, returning back to The Shire with 1/14 of the gold as he was promised, and continues to live happily in his hobbit hole.