They hope to kill the dragon and take back the Mountain and the vast treasure that the dragon had stolen. (Honestly, just read the book.)
The main conflict in The Hobbit is trying to regain the Lonely Mountain from Smaug the Dragon.
Thorin Oakenshield lived in The Lonely Mountain, but he and the other dwarves have lived in exile since the dragon, Smaug, took the Lonely Mountain.
There are no dragons in The Lord of the Rings. The dragon in The Hobbit lived in the Lonely Mountain.
Thorin Oakenshield lived in The Lonely Mountain, but he and the other dwarves have lived in exile since the dragon, Smaug, took the Lonely Mountain.
Thorin wanted to claim the long-forgotten treasure of the Lonely Mountain, because it had once belonged to the Dwarves, and was taken from them by the dragon Smaug. He was also the rightful king of the Lonely Mountain.
The mountain where the dwarves use to live before smaug came and claimed the mountain and its gold.
Smaug is the dragon that has laid waste to the Lonely Mountain and terrorized Laketown for many years. He stole the dwarves' treasure that lived in the Lonely Mountain.
The name of the dragon was Smaug. He was a winged fire drake, and he drove Thrain and Thror from the Lonely Mountain. In Appendix A of The Lord of the Rings he is given the title of Smaug the Golden in the story of how he took over the area around the Lonely Mountain.
Because Thorin is the grandson of the King of below the Mountain (Thror). They are happy to see him and the other dwarves.
ice dragon+Earth dragon=Mountain dragon
By 'the hobbit', I'm supposing you mean Bilbo Baggins in The Hobbit? If so, he faced Smaug the Great Dragon, King of the Lonely Mountain.
The dwarves were searching for the secret back door that led into the Lonely Mountain. They wanted to enter this way because the front gate was guarded by the dragon Smaug.