Its usually 16% incendiary, shock, or corrosive.
Do I need a incendiary gun to get the bonus? Same with others?
Do you get the bonus using normal bullets?
If so, if i get all 3 on artifact is that essentially +48 damage?
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No, the bonus damage only applies to the element it boosts. All 3 bonuses would apply 16% boost to each element as used. 
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They also come with damage for a certain weapon type. like plus 17% shotgun damage, plus 16% corrosive damage…so that would mean you have 33% more damage with a corrosive shotgun