Fifteen day-hike trails begin within a short drive of the visitor center [1]. Of these, only Grand Wash, Capitol Gorge [2], Sunset Point, and Goosenecks are easy. The others involve moderately strenuous climbs and travel over irregular slickrock. Signs and rock cairns mark the way, but it's all too easy to wander off if you don't pay attention to the route.
Although most hiking trails can easily be done in a day, backpackers and mountain hikers might want to try longer trips in Chimney Rock/Spring Canyons in the north or Muley Twist Canyon and Halls Creek in the south. Obtain the required backcountry permit (free) from a ranger and camp at least one-half mile from the nearest maintained road or trail. (Cairned routes like Chimney Rock Canyon, Muley Twist Canyon, and Halls Creek don't count as trails but are backcountry routes.)
Bring a stove for cooking because backcountry users are not permitted to build fires. Avoid camping or parking in washes at any time—torrents of mud and boulders can carry away everything!
Links:
[1] http://www.moon.com/destinations/utah/the-escalante-region/capitol-reef-national-park/exploring-capitol-reef
[2] http://www.moon.com/destinations/utah/the-escalante-region/capitol-reef-national-park/sights-along-hwy-24