A 13 amp plug will usually come with a 13 amp fuse. This is the maximum amount of current an appliance can draw before the fuse blows.

When the fuse blows it's a simple job to pull the old one out with a small screwdriver and replace it. (see section on voltage/continuity tester to see how you can check fuses)

Some appliances however will come with identical plugs which have a lower rated fuse. 3 amps or 5 amps for instance. It is VERY IMPORTANT that you replace like with like. Do not use a 13 amp fuse in a appliance that stipulates a 5 amp fuse, for instance.

A fused spur to an individual appliance may form part of you household wiring.(they may also have a switch)These wall mounted fittings have a fuse inside which may need replacing.
Switch the power off first.
Use a fine flat screwdriver in to pull it out the fuse holder to reveal the fuse.
Some fuse holders will have a small retaining screw. Unscrew it and the fuse holder will come out

Replace the fuse with the same rated fuse.