I live in Cincinnati. I have a vented crawlspace with a dirt floor with plastic over it and with no insulation. I believe I need to add insulation in between the floor joists. Do I use insulation with a vapor barrier or without? If I use a vapor barrier which side should it be on?
Great question. Insulating your floor is going to make those chilly Cincinnati winters much more comfortable on your feet. I would recommend using unfaced fiberglass batt insulation. Choose insulation that is as thick as the floor joists are deep. So if you have 2 x 10 floor joists, choose 10-inch thick insulation. Support the insulation with insulation hanging wires which are spring-like wires that flex and are bent so that the ends dig into the joists to hold up the batts.
As for your vapor barrier question, vapor barriers always point towards the heated space which in your case would be the underside of the subfloor, however, in an existing home, it's almost impossible to get vapor barriers in well enough to seal off moisture. Plus you already have vapor barrier on the crawlspace floor, so it's really not worth it.
Finally, make sure the insulation is fluffy and not compressed, as that is what makes it most efficient.