Two possible access routes but both involve Highway 82:
From US HWY 24 between Leadville and Buena Vista, take the State HWY 82 west, around Twin Lakes for 14.5 miles for the turnoff left (south) onto the South Fork Lake Creek road. (FR391)
From Glenwood Springs/Aspen, drive on State HWY 82 through Aspen and continue driving one of Colorado's most thrilling passes to the summit of Independence Pass. Continue over the pass, down the east side and from the final switchback that drops you down to valley level, it's about 4.5 miles to the turnoff for the South Fork Lake Creek road (FR391).
Once you turn onto FR391, drive over the new bridge (placed summer of 2014) that crosses the Lake Fork and perhaps stop to admire the narrow gorge the bridge is built over. Continue driving through private property initially for another 2.7 miles or slightly further to where the road forks for Sayres Gulch (FR 382). Park in this vicinity. The road to Sayres Gulch will branch off to the right. The road you want for UN13,460 East and Sayres BM continues more directly toward some trees and a crossing of the creek. Our last visit to this road, the Forest Service had closed it with a locked gate not very far up. They have closed this road for restoration purposes. Even if you had 4WD and the gate was open, you would not get very far anyhow because the condition of the road had deteriorated so much.
The road up Sayres Gulch (FR 382) was still open up to the wilderness boundary as of 2003. At this point, you'll want to have 4WD with good clearance. It will come in handy for getting across some rough sections of the road as you approach the wilderness boundary. If you don't feel comfortable with these rough sections, park where you can to begin your hike. The distance up to the wilderness boundary and parking in an open meadow is about 1.75 mile.
There is a good, primitive camp location a short distance before reaching the TH. See coordinates provided. Otherwise, if you want something less primitive, here are some other suggestions:
On the east side of Independence Pass, designated Forest Service campgrounds include Parry Peak and Twin Peaks. There are also numerous primitive sites all along Lake Creek. One of the best is here: N 39° 04' 54.99" W 106° 32' 21.86". This is where a diversion tunnel empties out into the Lake Fork and is just under 2 miles west of the turnoff for the South Fork of Lake Creek.
On the west side of Independence Pass, there are designated Forest Service campgrounds at Difficult Creek, Weller, Lincoln Gulch and Lost Man. There are no good primitive sites, but you may be able to use the trailhead parking area across from the Lost Man CG.