From the intersection of US 285 and SH 9 at Fairplay, drive south on US 285 for one mile to CR 18. Turn west onto the county road. In about four miles, you'll come to National Forest land. Drive west past the Horseshoe CG , then the Fourmile CG. Both are rather small and have limited number of sites. 2.5 miles past the turnoff for the Fourmile CG you'll arrive at the old mining townsite of Leavick where there are still some old buildings. Park in this vicinity for passenger vehicles. 4WD may be able to continue up the road as much as another two miles. Much of the land around here is privately held, mostly old mining claims. Respect any private property postings. Mt. Sheridan is on privately held land. Much of the route up to Mt. Sherman is also on privately held land. Fortunately, at this point, there have been no attempts to block access to these peaks.
As mentioned above, there are two National Forest Campgrounds on the drive in - the Horseshoe and the Fourmile. It appears that the Fourmile CG is always first-come, first-served while the Horseshoe has sites that can be reserved on Recreation.gov during the "reservation season." Other than these two campgrounds, you may find a primitive site on the north side of CR 18 at Horseshoe and some other primitive sites on the south side of the road, a short distance back east from Horseshoe CG.