Direct quote from the wikipedia article of Mjölnir
hammer of Thor, a major Norse god associated with thunder. Mjölnir is depicted in Norse mythology as one of the most fearsome weapons, capable of leveling mountains. In his account of Norse mythology, Snorri Sturluson relates how the hammer was made by the dwarven brothers Sindri and Brokkr, and how its characteristically short handle was due to a mishap during its manufacture.
As to how it's made it is said on the wiki that it was made as a bet to show Loki that they could make a item more beautiful than those of the Sons of Ivaldi. Although they didn't intend to make the handle as short as it is. the reason for that is that Loki did not intend to let them win and therefor tried to hinder them during forging.
Finally, Sindri puts some iron in the forge and tells Brokkr not to stop pumping the bellows. Loki comes a third time and this time bites Brokkr on the eyelid even harder. The bite is so deep that it draws blood. The blood runs into Brokkr's eyes and forces him stop working the bellows just long enough to wipe his eyes. This time, when Sindri returns, he takes Mjöllnir out of the forge. The handle is shorter than Sindri had planned and so the hammer can only be wielded with one hand.
And as to how Thor got Mjölnir if my memory isn't wrong then it was because Mjölnir was given to Odin as a gift. When Odin found out that Mjölnir deemed Thor worthy to wield him Odin gave Mjölnir to Thor. For he him self didn't need the hammer.