The Forest Service Website says that the North Sheep Mountain Trail "is more of a navigation exercise than a trail." While this isn't exactly accurate this trail is a badly eroded gash quickly becoming a stream bed in some places. However, it is fun for mountain biking (down).
From a large cairn on Johnny Park Road, head up hill briefly before an almost continuous downhill run almost all the way to the North Saint Vrain Creek far below. When you get to a trail intersection turn left onto the Button Rock Trail.