I usually go by car.
Seriously - and no one goes this way any more for some odd reason - get off at the Freeman Ave. Exit. Go straight throught the light. Go past 8th street, cross over the US 50 bridge. The road will bear left. It is now called Mehring Way. Take Mehring Way to Pete Rose Way (it only goes left). Turn left. Go through all the lights and past PBS. Pete Rose Way deadends into the Freedom Center Garage ($12) or Lots B & C ($10). GO to the Plaza level and its a 2 block walk on to the GABP grounds. I think its a better alternative to the Broadway Garage since you aren't crossing the street twice and being run over by the crazy drivers.
That is has been the best way to the ball park since I've been a kid coming down from Dayton.