It looks like Nozspark has beaten me to it, but my diagrams are better
This is a typical ring with a fault on it causing a short between live and earth (for example)
The first thing to do is split the ring at the mid point (or as close as you can get)
The mid point of this ring is socket 7, so you would remove that socket front making sure all of the wires are seperate.
Then test each leg of the ring at the CU. It will show that the right leg of the ring is ok, and the fault is on the left leg, somewhere between the CU and socket 7.
The next thing to do is to split the faulty half of the ring again, which would be at socket 11.
Then test the left hand leg from the CU. This will now show no fault, indicating the fault is between sockets 7 and 11. You can test this section of the ring to make sure.
Then split the faulty part of the ring again. In this example it would be at the junction box for socket 9.
then test the section between socket 7 and the junction box, and socket 11 and the junction box.
This will show the fault is between socket 7 and the junction box.
Keep doing this until you have tracked the fault to between two points on the ring circuit. In this example between socket 8 and the junction box for socket 9.
Replace this part of the circuit, put it all back together, and retest everything to make sure the fault has been removed.