From the Lead King Basin trailhead, hike north along a good trail to Geneva Lake. The valley is bursting with color in the summertime, and features a multi-stage waterfall as you climb up toward the lake. Several switchbacks position you level with the waterfalls long before you actually reach them, at 1 mile. Continue along the trail a second mile until you reach Geneva Lake, a short ways past a pond. Cross the creek at the lower end of the lake on a large log jam. Hike east up the hill 100 to 200 feet to catch a small trail which does an ascending contour around the east side of the lake, at least 100 feet higher than the lake. This may be a deer trail, but it works well. While on this trail, you can see the lake through the trees much of the time. Follow this trail as much as possible, until you intersect the main trail again, ascending above Geneva Lake. Rejoin the main trail as it doubles back on you going south.
Variation: Instead of crossing below Geneva Lake on the log jam, you may stay on the main trail around the west side of the lake, and try crossing the creek above Geneva Lake. This route failed us in mid July of 2005 because the stream was running too full and deep to make a safe crossing. Further above, there were no crossings either. The runoff was just too much volume, and there were no narrow spots to jump across.
Once you are safely on the main trail way above the lake to the east, continue south and east until you reach a small creek descending from the south face of Hagerman Peak. This is at about 11,480'. Leave the trail here. Follow the creek for about 0.5 miles as it ascends north and west. Follow the creek to its end.
The entire remainder of the route is now in front of you to the north. Pick a route through some rocky ledges, and onto Hagerman's south face. Choose either of two shallow gullies and scramble straight up the gully for 1,200', aiming for Hagerman's east ridge. Once you are on the ridge, the steepness eases and you can hike leisurely to the summit.
The total elevation gain from the trailhead is about 4500'. At no point is the climbing difficult, so you can figure on making good time as long as you don't lose the route. Descend the same way, or by the Southwest Ridge route.
Descend from Hagerman's summit east for 0.4 miles to Snowmass Peak, before returning the way you came. The views down to Snowmass Lake, east to the Maroon Bells, and back to Hagerman Peak will take your breath away.