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 left for Sayres Gulch (FR 382). Stay on FR391. The 4WD road up McNasser Gulch will turn off to the right in about an additional .6 mile. Stay on FR391. In another 1.3 mile, you'll come to the turnoff on the right for Peekaboo Gulch. There's a cabin in this vicinity and private property belonging to old mining claims. Do not attempt to camp in this vicinity. In a short distance, you will cross Peekaboo Creek. Just past the creek crossing is another private cabin. Do not attempt to camp anywhere near this location. Our son and a friend were trying to find a camp spot in the dark near the creek several years ago and the owner of the cabin fired warning shots at them.
From where the road turns off for Peekaboo Gulch, it's another 1.2 miles to the trailhead and wilderness boundary. The last several hundred yards may become more difficult and this is where the additional ground clearance will be helpful. Our last drive up this road was 2003. Conditions may have changed and we would not be surprised to find the Forest Service has pushed the road closure spot back further down the drainage.
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, just off the highway. 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.
As you drive in on FR391, there are primitive sites you can choose from once you're past the initial area of private property, though in the past, we've observed some efforts by the Forest Service to close some of those primitive spots. It's possible to camp at the trailhead where there are scattered willows and a few other spots before the TH.