Escalante has only one developed trail. You'll find it at Lower Calf Creek Falls, which lies between the towns of Escalante and Boulder on Highway 12. Visitors hike along a 5-1/2-mile (round-trip) developed interpretive trail to reach the shady pool at the base of the 126-foot falls. The hike is considered moderately difficult and serves as a good introduction to the Escalante Canyons.
Beyond that, you better know how to read a topo map, because hiking in the monument is almost completely cross-country. Most of the monument is still remote and primitive with undeveloped hiking routes and roads. But rest assured, excellent day hikes, backpacking, and backcountry opportunities are available.
Because of changing weather, hiking, and road conditions, it is difficult to recommend any given area for backcountry travel. Stop by the visitor center, and hash it out with the staff there. They can give you the scoop, and sell you the right topo map to get you on your way.