Just to set the record straight: There's far more acreage in national forest wilderness areas, at least in the western US, than in national park wilderness area! All but a very few high-impact areas in national forest wilderness areas are open to dogs as long as they are under control. More and more national forest wilderness areas are requiring leashes on at least some trails.

In national parks, dogs are forbidden on all trails, not just in the wilderness sections. (The one exception that I know of being the PCT in Mt. Rainier and North Cascades National Parks.)

Lori is correct in that hiking dogs need conditioning, just like hiking people! Hiking dogs also need training. A series of good obedience classes are a must. Crate training is a big help in getting a dog used to staying in a tent. Agility training is really helpful in giving a dog confidence in tight places. Dog boots are needed in areas with sharp rocks and pumice (some of which are better avoided with a dog). And your first aid kit needs a few dog-specific items.