From Cloudcroft, turn south onto NM130. Continue for 1 mile and turn left (east) onto Forest Road 24B (just across the road from the Deerhead Campground entrance. The entrance will be on your left hand side.
Such a lovely place to camp! It was well kept and had a big covered area with plenty of tables for many guests.
A couple of fire pits, a (very clean) restroom (for boys and girls), about 8 or so parking spots, and plenty of room to stretch about if you feel so inclined.