Not sure if this is a state park fee use area. Personally, just to be careful, I picked up an Alamo Lake State Park day use permit before heading towards the trailhead.
It is about two miles of pure jeep trail hiking from the pullout / old campground to the arch. Because I was doing some other things in the area, I approached the arch from the northeast, which gives a good profile shot if it is mid-afternoon. It is a steep & slippery climb up the northeast face, but not too bad. Once on top, turn left along a narrow ledge to the arch opening. The arch itself is tiny, and delicate -- do not climb on it. There is a safe shelf to sit on the arch's southwest face. If you peer through it, towards the northeast, with a mid-afternoon sun, you can see the arch's shadow, complete with sunny spot, on the desert floor. I've never experienced that before! Definitely makes it worth your time.
The arch's southwest slope is mild, and I descended that way, following a fairly obvious foot trail, back to the jeep trail. You could also go up the southwest face, but then you would miss the profile shot, unless you went down the steep & slippery northwest face. Personally, I'd do it the way I did: Counter-clockwise.
Check out the Official Route and Triplog.
This hike is listed as One-Way.
When hiking several trails on a single "hike", log it with a generic name that describes the hike. Then link the trails traveled, check out the example.