Well, there's two ways this could go with the current spines model (if we ever get different animations, other explanations may arise):
1. The person rearranges their bone structure into spines that pop out. Only problem with this is that they'd have to, say, debone one arm cause they're whacking people with their humerus.
2. The person can generate excess bone matter, and that's the spines.
Either way, there also needs to be some explanation for why they don't bleed like mad with bone popping out of their skin.