SST is a New Mexico classic: chunky rocks, tight switchbacks, rugged, and tough. If you are looking for an easy, smooth trail, the west side of the river is not for you; try Dona Ana Trail instead.
There is a small parking area a short way up the arroyo from the road. This will generally be accessible by street cars depending on the condition of the arroyo. There is a larger staging area further up but this may require high-clearance or 4X4.
Head up the road; there are a couple of possible routes to reach the point where singletrack begins. The singletrack contours along the canyon then briefly joins a road before dropping down into the main drainage. Once you hit the arroyo, follow it west for about 750 feet watching for the trail on your right. Once you see this, turn back to the northeast and follow the trail as it gradually rises through exceptional switchbacks.