It's the same way you can go from nailing two pieces of wood together with a hammer, to slicing up fish with a knife. You'll also note that when your meatheaded tank "picks up a staff", he's initially level 1. It's not like he picks it up and all the information springs into his head. It's more that a staff is the proper tool for slinging fireballs, and he learned how to do so the same way he learned how to swing an axe: By practice with it.