Finding the trail is the hardest part!
Skeleton Mesa is the large mesa to the west of Kayenta, north of US 160, and north of Marsh Pass, which is the area to the west of Kayenta approximately near the Anasazi Inn. It is similar to Black Mesa, but geologically very different and it has had less human intrusion than Black Mesa. Unlike Black Mesa, there do not appear to be roads on Skeleton Mesa, and there has not been any clearing of the vegetation for grazing. There is also no coal mine! There is a trail which ascends a ramp on the eastern side of the mesa, and once found the trail is pretty easy to follow, but finding the trail is the hard part. However, if you have been there once, it should be pretty easy to find.
From the parking area or trailhead, hike cross-country west towards the large ramp, or monocline, that can be seen to connect with the mesa. This ramp is distinctive, and may be the only part of the intact monocline to actually reach the mesa top. This image looks at the ramp. As you hike west, you will reach a small graded (when I met it) road. Depending on where you are, you will want to follow it north for a short time to reach a small seldom used, but noticeable, two track on the west side of the graded road. If you take this two track, you can go directly to the trailhead where the tracks loop around at the base of the trail. If you can't find them, or have met the better maintained graded road north of the two track, good luck. Things change out here, and unfortunately, details are hard to pin down. Coordinates are the best way for an outsider to access the area. The road junction is not visible on the satellite image, nor is the trailhead, but I interpreted the trail end (I met it going down) to be roughly: 36.74356, -110.39143. Hopefully, that helps and you are not completely lost. You basically have to know where you are going and have some sense of direction. I found the trail by accident, but had an easy time getting close to it. Coming down was essentially a breeze.
If you have no GPS, you can find the trail by looking for where the main body of the ramp reaches the plain and attempting to locate the trail on it. If you go too far north you will encounter an erosion basin, and too far south you will encounter a large sandstone hill (as I did). I went over the hill and dropped into a drainage before ascending a slightly lower sandstone ramp. Eventually I cliffed out, but I hugged a small cliff and found a way up to the main body of the ramp, and that is where I met the obvious cairned trail. If you go too far north, you will probably not find the trail, but you should know this when you see the massive teardrop shaped basin. The lowest sections of trail are braided and confusing, so you may not even be aware you are seeing it. This hike really needs a GPS enthusiast to record plots for the trail as they descend, but not while going up as that will confuse people if trying to locate the trail with them.
OK, let's pretend you had an easy time finding the trail and are now hiking up. You have it pretty easy, and can follow it as it ascends to the top of Skeleton Mesa. The top can be considered the large sandstone area near the group of Ponderosa Pines. The trail continues on to the pinyon and sage covered mesa, but again, finding it is hard unless you know the way. There are erosion gullies and they look like trail at times. If you found it, the trail crosses over the mesa all the way to Utah, I am told, but I know nothing more about it once you are about 1/4 mile beyond the Ponderosa Pines. Return the way you came, and hopefully you'll have an easy time hiking down. I did, and went right to my car, but that was partly due to me following my foot steps.
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WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.