Terrapin Mountain is one of many mountains along the Blue Ridge Parkway that receive very little attention because there isn't a trailhead directly off of the parkway.
The easiest way to get to Terrapin Mountain is from the appropriately named Terrapin Mountain Road which turns North off of VA-122, between Bedford and Big Island. The trailhead is a couple of miles up this dead end road on the right, where a gate blocks an old Forest Service road. Despite the no parking sign you can park there and hike up the road. Make sure not to impede the road!
To achieve the summit head up the old road straight past the closed gate. After about half a mile you will start seeing old road cuts leaving the main "road" on the left. One of these, heading directly left, is even blazed orange/yellow. This trail to the left will lead you around the base of the mountain and up into a drainage basin between Camping Ridge and White Oak Ridge. It is possible to climb Terrapin this way but it would be a long haul.
Instead, watch for a cairn on your left where the road veers right. You will also see orange and yellow blazing here. Head uphill onto this trail. The trail is not well marked and often overgrown. Pay attention as it zigs and zags its way up to the ridgeline. The blazing can be infrequent and the trail makes odd cuts as it (sometimes) follows old road cuts. If in doubt, simply head straight up to the ridgeline. Once you achieve the ridge the trail is easier to follow as the ridge is fairly narrow. Before you reach the first of many false summits watch for the trail to take you off to the right where there is a rock outcropping with the best view you will get the whole hike. This view looks north towards the parkway and Thunder Ridge. You will also be able to see Camping Gap and Apple Orchard Mountain. Continue up to the first of 4 or so false summits and after a mile or so the trail will reach the true summit. Some blazing indicates that the trail cuts off to the right just before the summit so simply stay on the ridgeline until you reach the top. The trail drops off to the west towards Camping Gap after the summit.
None, the trail and parking are free. There is a no parking sign that has been posted at the trailhead for years. You will have no trouble however as long as you don't park in the road. There is a convenient pulloff just in front of the gate. While it isn't likely you'll be sharing the trail with too many others, please be considerate and park in a sharing manner.
As most of the mountain is within the George Washington National Forest, most of the rules and regulations pertaining to camping in that area apply. There isn't much flat ground and there are no developed campsites so camping isn't recommended.