Drive Highway 130 to the Lake Marie West Trailhead (see Getting There). There are several trails around, and the one for Medicine Bow Peak is well marked with a sign. Otherwise, just follow the trail that goes up the hill to the northwest and behind the ridge (Schoolhouse Rock, the Diamond, etc...).
This trail ascends the Medicine Bow Peak ridge up and behind the points on the ridge which are Schoolhouse Rock, The Diamond, Old Main, etc... The trail's name is Medicine Bow Trail, and it's well marked on the accompanying TOPOZONE map. The trail is fairly steep at first, but is thereafter quite gradual, especially after attaining the main ridge near the peak. If you want to bag the 'points', doing so is highly recommended and offers tremendous views of Lake Marie, Lookout Lake, and Mirror Lake. In the winter, be wary of cornices! Follow the obvious cairns along the trail until you reach the summit of Medicine Bow Peak. From here, continue east back down to the Saddle Between Medicine Bow Peak and Sugarloaf Peak. Follow the trail between Libby Lake and Lewis Lake, and then proceed north along the designated trail towards South Gap Lake. The actual trail name is North Gap Lake Trail. The best route up Browns Peak from this side is the west side. The suggested starting point for actually climbing is just between the incline and South Gap Lake.
General hiking boots, water, and proper clothing is sufficient for summer hiking. Trekking poles make things easier, too. For winter, crampons and/or snowshoes, ice axe, and warm clothing is essential for the steep climb.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.