Leaving aside Dampe's great answer, another answer was quite simple: a dash of nepotism.
Jabba was the nephew of Jiliac, the head of already-powerful Desilijic kajidic (src: Rebel Dawn by Crispen, Book 3 of Han Solo Trilogy).
He became a powerful crime lord because his family was powerful crime lords, and he showed them he was worthy of taking his place at leadership.
As an aside, Jabba's Hutt physiology offered its own direct benefits:
Long life
Natural protection (Hutts have tough hide and are very hard to kill overall)
Resistance to Jedi mind tricks