Ranger-led tours
Slaughter Canyon Cave
Also known as new cave, is a separate "wild" cave that can be reached on a ranger-led tour. this cave is in the detached part of the park containing slaughter canyon, reasonably enough, and requires a short but testing hike aboveground before the cave entrance is reached. several spectacular formations are visited on this tour.
Spider Cave
Is another "wild" cave that requires considerable crawling -- not for the claustrophobic. the visitor who pays the fee and endures the entrance crawl is rewarded with up-close views of a number of delicate and remarkable formations, perhaps the most famous of which is "the mace."
The park offers scheduled tours of "wild caves" that give the visitor a taste of what visiting an undeveloped cave is like. All require reservations and have fees; see the link below for details. Visitors should be in good health and be prepared for some hard work, possibly including crawling in tight spaces depending on the tour; wear clothes that can get dirty -- seriously dirty.
backcountry caves
The park's policy toward access to caves in the backcountry varies from year to year. Most backcountry caves are closed completely to the public except on special occasions. However, Goat Cave, Ogle Cave, Corkscrew Cave, Christmas Tree Cave, Wen Cave, and Lake Cave have all been open to the unescorted recreational caver at various times on a permit basis. Most of these caves have significant vertical sections and require proficiency with rope and ascending/rappeling gear. Know what you're doing before even thinking about getting a permit for them.
hiking
There are several surface trails in the park that afford the hiker a first-hand look at the ruggedness of the terrain. No mountain bikes allowed. Several are in the Slaughter Canyon area. Day use is unrestricted, but the backpacker planning an overnight stay must obtain a free permit from the park. Campfires are prohibited in the backcountry; use a stove, and take plenty of water. Good hiking boots are a must, and long pants are preferred to shorts owing to the remarkable variety of spiny and thorny plant life that can poke a good-sized hole in you.