I work for USFS, you've gotten good advice above. Check in at the local ranger station and get a map, and inquire about closed areas, if any. Don't shoot in or near a developed campground, other campsites, parking area, or on or from or across any road or trail, or into over water. Don't shoot the trees, chipmunks, or without a safe backstop. Pick up all your brass, and don't shoot appliances or bottles, take it all home with you. Don't shoot or possess tracer ammunition, tannerite, or any munition that could start a wildfire. Have a bucket, axe, and shovel, just in case you do.
Sounds like a lot, but just common sense for safety, and when 1,000 people shoot bottles and trees, it really tears up an acre or two of your public land, so that's why the rules are there. It's your public land, so enjoy it and treat it responsibly so your grandkids can do the same thing someday.