Scotland has a very progressive Outdoor Access Code which essentially guarantees everyone the right to access most land in the country for recreational purposes so long as they act responsibly. You'll pass a few fences that you must open and close behind you or else the ubiquitous sheep will get out. (Do not let the sheep get out!)
From the B7062 road, go south on Kirkburn Road. There is a small park near this intersection including a trailhead for several hiking trails in the Cardrona forest. The path climbs steeply for several miles, but most of the climbing is on the forest road. At about the three-mile mark, the road will stop at a freshly cut section (as of 2014) of forest. Continue climbing up until you intersect with a singletrack at the top of the ridge.
Once you reach the top of the ridge, turn right onto the singletrack. This is probably the most challenging part of the ride, but it is not overly difficult. Anyway from the ridge you'll have great views of the rolling Scottish countryside to distract you. Continue following this singletrack until the 4.3-mile mark. Then the path takes a sharp right and widens slightly. Keep the forest directly on your right.
After about a third of a mile, the wide section ends at a four-way intersection. Turn right to follow a singletrack along the fence line. Much of this fence line is made of ancient stone fences. From here, the climb continues for a short distance before you're rewarded with a three-mile, mostly singletrack downhill section almost all the way to the town of Peebles.