Shanzar had declared himself the Sorcerer Supreme of his dimension, the "Strange World". As he destroyed or assimilated everyone in his world, he sought new worlds for conquest and adventure.
To enter Earth-616 (or apparently any other dimension), he required a strong host body. He acquired one when he took over the body of the Hulk which transformed him into the Dark Hulk. Shanzar entered worlds through mystic portals and grabbed his prey with large expanding tentacles. He then took mystic command of this "host" and could safely enter other dimensions. When separated from his host, he appears as a spirit form. Bruce Banner's psyche, along with Doctor Stange and the Sub-Mariner, were able to defeat Shanzar and return him to his dimension.