Drive out the Steese Highway to the intersection with the Elliott Highway (you come to a four-way intersection, the Elliott is straight ahead, the Steese turns to the right). Drive up the Elliott for a little over three miles to just past the intersection with Old Murphy Dome Road. There is a little parking area to the right. Park there and head on up the road that goes uphill.
Follow this road for about a quarter-mile or so. Then there is a double track going straight up the hill to your left. Follow it up a hill (about a quarter-mile or so), where it levels off, drops down into a saddle, then climbs up again. There are several side tracks, cat trails, etc. that you can explore. At any rate, you come to a fork in the trail before you get to Pedro Dome, which dominates your view of the eastern horizon. Take the right fork.
This trail drops down the hill, levels off, then comes to an incredibly difficult, heart-stopping, two-mile descent which finally puts you out behind Pedro Monument. WARNING: this descent is EXTREMELY dangerous and should not be attempted at speed by a beginning rider. Very serious crashes have ocurred on this hill and it is not for the faint of heart. If you are at all doubtful of your bike handling abilities, take it slow and easy. You'll get to the bottom in one piece in due time.
Once you get to Pedro Monument, turn right at the Steese and take a leisurely six-mile downhill road ride back to the intersection with the Elliott. Then it's three miles of of somewhat uphill riding back to your car. Total distance is about 15 miles.