You're best best is to call the Backcountry Office at Yellowstone : 307-344-2160. Or, you could write them, if that's easier -

Backcountry Office
P.O. Box 168
Yellowstone National Park, WY 82190

The park asks that you give at least 48 hours notice before you set out, so you really want to call ahead. We've got some information here about hiking in the park, including back country tips.

The National Park Service has some information on their website too, including back country videos specific to the time of year you'll be hiking - summer or winter.

Yellowstone Backcountry Trip Planner