Check out geobetty.com or stop by a local bike shop and pick up a comprehensive map. It covers almost all the El Paso trails. I'd recommend the northeast trails. Redd Rd and the west side of the park have some great trails, but are more rocky and technical.
The trailhead can be a little tricky to find, but worth it. Basically get off 54 on MLK and head north. You'll go under the highway and then take the first left into a neighborhood and go all the way to the end and park. There's a small park there. Head up the flood wall or the trail on the left to access the trails.