Whether coming from the east or west on I-70, take the Minturn exit # 171 and head south on US24 to the town of Minturn. When the highway comes into town at the north end and makes a fairly sharp right turn, it's about 3.5 more miles south to the turnoff on the right for the Tigiwon Road (FR707). The turnoff is just before the highway crosses Eagle Creek. If coming on US24 from Leadville, the turnoff is after the last switchback as you descend from Battle Mountain. After that switchback, the highway crosses the Eagle River and the turnoff will be almost immediately after that crossing on the left.
Once on the Tigiwon (on some maps labelled Tigwon) it's a long drive on a graded, gravel road that meanders through countless turns and switchbacks to the trailhead. There are beautiful stands of aspen and open meadows. Total distance is about 8.5 miles. About 6 miles in, there's a small campground that is not listed on the White River NF website, just beyond the Tigiwon Community Hut. Overall, the road can be somewhat rough, but most passenger vehicles should be able to make it to the TH. Cross-overs & standard SUV's would be a safer bet. This road may not be open until mid-June some time. Check the White River National Forest website for more info. Both the Half Moon trail and the Fall Creek trail take out from here. Be careful to correctly identify the trail you desire. There is a small, national forest campground on a spur road from the trailhead. This will almost always be filled on summer weekends. There's only 7 sites. Primitive campsites along the Tigiwon Road are limited. Parking can also be a hassle on weekends with so many climbers coming to do Mount of the Holy Cross, you may end up parking along the side of the road as much as a quarter mile back from the trailhead, even on a Friday evening.
There is a very small campground (Half Moon) at the trailhead area which was re-worked several years ago. There are only seven sites and a fee is charged. The campground is first-come, first-served. Some sources indicate a campground near the Tigiwon Community Hut. The White River NF makes no mention of it. Camping at the Tigiwon Hut is prohibited, but on Google Earth, you can see some primitive sites just up the road from there. Attempt to camp at your own risk. The Half Moon CG can be expected to be fully occupied on any summer weekend. Also, because the Half Moon Pass trail is the access to Mt. of the Holy Cross, and that summit is one of the more popular 14er destinations for Front Range peakbaggers, the limited trailhead parking fills immediately on weekends and later arrivals will find themselves having to park a substantial distance back down the road.