Volstagg's origin beyond being a member of the Asgardian race, a warrior and adventurer, and a friend of Thor has not been revealed. Volstagg is fairly advanced in age for an Asgardian, and it has been suggested that he was a highly respected and feared warrior in his prime.
In a sense, Volstagg's entire career has been one long origin story. The character was first introduced in a "Tales of Asgard" filler in Journey Into Mystery #119 (August 1965), the magazine carrying Thor's Asgardian adventures. As originally envisioned by Jack Kirby, Volstagg was a huge, bumbling oaf much given to boasting and bragging: the last into battle and the first to claim victory (usually undeserved). Referring to himself as "The Lion of Asgard", he usually caused more problems than he solved and seemed totally unaware of the chaos that almost always followed in his wake. A flashback revealed in Captain Marvel #42 tells how a drunken Volstagg incurred the wrath of Odin by spilling the secrets of the first Frost Giants to a younger Thor. Strangely enough, he was considered a trusted and worthy comrade by his closest friends and allies, Fandral the Dashing, Hogun the Grim, and Thor.
In his first appearance, Volstagg joined with the Warriors Three in Thor's quest for the power that had cracked the Odinsword of Asgard. Volstagg then helped repel the attack of the Flying Trolls of Thryheim, although he cowered for a lot of the fight, helped defeat the forces of Harokin, was lured into a trap by the dragon Fafnir who used an illusion, and defeated Mogul of the Mystic Mountain.