Electricity is dangerous and can be hazardous. In doubt? Call a qualified electrician.
The easiest way to fit an extra socket to an existing ring circuit is to add a spur. A spur comes off the ring circuit via a junction box, or more usually via an existing socket - which ever method is easiest. See also Adding a spur from a junction box.
If you intend to run the spur from an existing socket, firstly check whether the socket is suitable to supply a spur.
SWITCH OFF ELECTRICITY AT THE MAINS
Turn off the main supply on the consumer unit and ensure the socket you plan to use is dead. Remove the cover to the socket and inspect the wires going into the socket.
If there is one cable going to the socket, then that socket is already on a spur and is therefore unsuitable. If the socket has three cables going to it then it is already supplying a spur circuit and so again again is unsuitable. Once a suitable socket has been found, you can close it up for the time being and restore electricity until you are ready to connect the new socket.
See Installing a power socket for more details on how to fit a new socket. Once installed, it can be wired up. A new length of cable (2.5mm2) should run between the new spur socket and the existing socket. Wire the new socket up first, Red to Live(L), Black to Neutral (N), the bare wire should be fitted to Earth (E or 
) with some green/yellow sleeving covering any exposed bare wire.
SWITCH OFF ELECTRICITY AT THE MAINS
The mains supply will need to be cut again - switch off the master switch on the consumer unit and check that power has been cut. Next, unscrew the cover to the supply socket. The cable from the new spur will need to be fed into the mounting box (the metal box inset in the wall) this will require the removal of one of the circular punch out holes in the box.
Once the wire is coming out of the mounting box, remove the existing two cables from the socket and twist the conductors together with the new spur cable, i.e. red to red (live), black to black (neutral), and green/yellow to green/yellow (earth). Next, replace these wires into the screw terminals of the socket, Red to Live(L), Black to Neutral (N), Green/yellow to Earth (E or ).
Finally replace the cover of the sockets and screw them back up. Restore power and check the new spur socket and the spur supply socket are working.
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