From the I-70 - Copper Mountain interchange, take Colorado State Highway 91 south in the direction of Fremont Pass. It's about 7.5 miles south to Clinton Reservoir where there are two parking areas on either corner of the reservoir, just off the highway. You can't miss the reservoir from the highway.
If coming from Leadville, drive north through town on US 24 to the Us 24/SH 91 intersection. Continue north on SH 91 for 15.6 miles to the parking at Clinton Reservoir, passing the Climax Mine operation and topping out over Fremont Pass.
Note that the 1970 USGS Copper Mountain quad does not show Clinton Reservoir. It was put in after that date. The reservoir is open to public use and there are "fishermen" trails that appear to encircle it. The terrain up valley from the reservoir is clogged with willows and bogs. It appears to us that anywhere past the reservoir and on the south side of Clinton Creek is privately held, presumably by the Climax Mine and its' holding company.
The closest primitive campsites are 1.5 mile north on SH 91 at the road that turns east for Mayflower Gulch. There are a few possible overnight sites up that road. Otherwise, there are no close-by national forest campgrounds.