Elephant Butte is the highest point in Arches National Park. The peak is a flat-topped cap surrounded by towers and fins forming one big butte. The fins and towers of the butte contain many arches, including the very famous Double Arch.
Route finding skills are required to complete the trail. There are a lot of great web sites that give very detailed instructions. My favorite is Road Trip Ryan.
An entrance fee is required to enter the park, and a permit is required for the hike. Information can be found here.
There are some exposed areas, and rappelling equipment is required. Both rappels are bolted and are usually well maintained, but be sure to inspect the slings before descending.
Round trip time is 2-3 hours if you're familiar with the trail, longer if you have trouble finding the route or spend time on top of the butte enjoying the amazing view that few people get to enjoy.
Have fun and be safe!