Skill Cards: Many of them have extra text (if this text succeeds, draw a card). Does this apply to the person playing the card or the person making the test?
If a skill card adds a new effect on top of the normal effect of the test (e.g. "draw a card"), the investigator committing the card resolves it.
If a skill card modifies the normal effect of the test ("deal +1 damage", "discover 1 additional clue"), then the investigator making the skill test gets the benefit.