The Ridge Trail (not to be confused with the Ridge Trail at Penny’s Bend) is accessed from the Buckquarter Trail by parking at the end of Cole Mill Road. See that description to get trailhead details. Alternatively it is also accessed from the Knight Trail, but this is done seldom.
Describing it from the split on Buckquarter Trail, near the old Cole Cabin seen from the trail intersection, it heads due north, past another old cabin site on your right, and intersects the Knight Trail on your right. It turns west and crosses a small creek which can be robust after a long rain, and hits a trail split to the right, which is the Shakori Trail and continues on an old roadbed past the Group Campsites on your left, heading uphill to a sharp right turn where the Shakori Trail connects. This is not a loop trail, and most people return via the Shakori Trail.
At sunset, there can be interesting vistas by bushwhacking to the west (left) and standing on the ridge overlooking the Eno River, which usually cannot be seen through the trees below.