From the parking/camping coordinates provided at 10, 400 ft., look for an old mining road/trail directly across the creek that shows on the USGS quad. This trail switchbacks up the mountainside - first north, then SW. It may require some searching at first to find it, but once you're on it, it will be easy to follow. You will have to wade across Cunningham Creek. After the initial big switchback, the trail climbs steeply on the north side of the stream in Dives Basin, with multiple switchbacks. It took us about 2 hours to get to the old Shenandoah Mine ruins. We found a strange hole around here - about 30 feet deep that was perhaps the remains of an old exploratory dig. It looked more like a small, meteor impact crater. There was also a cable that stretched out way up onto the mountainside to some other mining activity.
Continue following the old trail higher into the basin. A large, yellow couloir sweeps down from the summit of Little Giant on the SE flank of the peak and pans out onto a large, rocky slope. This can serve as a quick descent route later on. Continue following the old trail where you wish toward the east ridge of the peak on mostly steeper tundra. Once on the east ridge, it's fairly easy walking over rubble to the summit. Overall time to the summit for us was just under three hours.
To descend, either return as you came or for variety, head west from the summit, dropping down a short distance to explore some more mining ruins very near the summit. From there, drop on down the yellow rock couloir to the SE, utilizing some nice scree slopes for quick descent. Then cross back over to join back in with the old trails in the upper basin and follow the track back down to Cunningham Creek. the relentless descent will take a toll on your feet, but you can cool them when you cross the creek.
An interesting side note: While exploring around the Shenandoah Mine, we found an old board that had a still legible stamp on it indicating it had been manufactured in Louviers, CO, which is between Littleton and Castlerock on Santa Fe. The date on the board went back into the late 1800's.