This place is beautiful. Just hiked the trail this morning. It starts at Sandstone Quarry Trailhead.
This is a moderate hike of 2.5-mile round-trip that runs up a canyon and over sandstone slickrock to a large natural depression (a "tank" or "tinaja") near the top of the Calico Hills ridge. The tanks were full of water, and there are great views of Calico Basin and the Las Vegas Valley just beyond the tank.
Calico Tanks Trail is one of the most popular hikes in Red Rock Canyon National Conservation Area, so I suggest going early.
Begin hiking north along the side of a gravel wash on a wide easy trail. The route is not always fairly obvious, but it works its way up the canyon following use-trails and traversing slick rock. The route is marked with cairns, and there were even cut steps in solid sandstone rock and built stone stairs on the steeper parts.
I suggest wearing gloves because it requires use of hands in some areas.
At the end of the trail, be sure to soak in the views of the Las Vegas 'Strip.'