what would happen if a human took dog pain medicine?

Depending on WHICH medicine it is.. the effect will generally be the same, if not much weaker.
Many animal pain medications are weaker versions of human medicines.
The safest ones are NSAIDs (think aspirin, ibuprofen)

You would probably want to stay away from any pet narcotics.. but in general medicines are prescribed based on weight, if the pet that was prescribed the medicine weighs less than you, then the effects will be less than they would be if you were prescribed the human equivalent.