Begin at Tennessee Pass Trailhead. On the southerly side of the parking area, just a few feet from Highway 24, you'll find a Forest Service "double post" trailhead sign. Take the trail starting at the "double post," then stay left to follow the marked Colorado Trail (small white triangles). Basically, this section of trail travels westerly by traversing several miles of hillside above Highway 24. At 2 1/4 miles the trail crosses through a small gulch at 10,400 feet.
Continue as the marked 10th Mountain trail takes you on a west and northwest route leading up the North Fork of West Tennessee Creek 1 mile to pass just north of Lily Lake (10,589 feet). Swing right (N) as you pass Lily Lake, cross the creek and a marshy area, then climb N for 1/2 mile to a low-angled clearing. From here the route climbs NW for 1 1/4 miles along the south side of the south fork of Slide Creek through a series of clearings until it reaches the south end of a large flat marshy area just below and to the south of the hut. The trail to this point can be confusing because of myriad snowmobile and ski tracks. In general, it follows the south Slide Creek drainage, but winds around enough to make "drainage tracking" hard. Your best insurance is to take great care near Lily Lake to identify the distinct cone of Homestake Peak. Using this as a landmark, pay attention to your map, compass, and altimeter to stick to the trail. The route is marked by 10th Mountain, but don't depend on trail markers for navigation.
You can see the hut from the south side of the last low-angled marshy clearing—it's perched on a low-angled hillside on the north side of the clearing. With poor visibility this could be a confusing area, so take care.