From the heart of Gardiner, MT follow E. Park Street east to where it ends in a hotel/lodging part of town.  Just beyond that is a small dirt area where the Gardiner and Yellowstone rivers meet.  This is the typical put in for this run.  Parking can be an issue during crowded summer months.  It is harder to get rafts down here than it is kayaks.  Use your own judgements while putting in and don't do anything illegal.