It should be easy...
Buy your new socket first, and examine it before fitting, the layout will be similar to the old one. Get a good brand like MK or Crabtree, easily available in your high street, not some cheap brand).
When you remove the two small screws at the side, the white face-plate should pull forward (don't pull hard, it should easily come out a couple of inches, but will be retained by the wires).
You should find there are three terminals. Two of then will be shielded by plastic to prevent accidental contact. One should be marked "L" and have one, or two, or three cable cores going into it, which will be covered in red plastic insulation (or brown, in a new house). The other should be marled "N" and have one, or two, or three cable cores going into it, which will be covered in black plastic insulation (or blue, in a new house).
One terminal will probably be brass with no plastic round it, marked "E" or with a digram of a Christmas tree on it. This is the Earth. It should have one, or two, or three cores going into it, which should be covered with green-and-yellow sheathing (this sheathing may be missing
but you can buy a small amount at the shop where you buy your new socket; it is very cheap). There may also be a short length of G&Y connecting the faceplate earth terminal to an earth terminal in the wall box.
The number of Red cores should be the same as the number of black cores, and the number of G&Y cores.
Observe all the wires for signs of looseness, damage or overheating (report back here on what you find)
Put the cores into the new terminals, deep, tighten firmly with a screwdriver of the correct size. Then go and have a cup of tea and a biscuit, when you come back tighten them again (copper wire is soft and can deform slightly to accommodate the screw).