The key to a good job when changing a plug is to cut the cable to the correct size.

Strip the outer insulation of the wire by scoring it with a sharp knife being careful not to cut into the individual cable insulation.

Plugs may vary. Pictured here, with a pretty standard plug I've cut:

-the earth cable to 35mm
-the live cable to 15 mm
-the neutral cable to 25 mm

Strip 5 mm of cable from each cable and twist the ends so they will be easier to locate in the terminals.

Unscrew the plug, loosen the terminals and loosen the strain relief.

NB some plugs have a simpler push fit strain relief which is quicker as you simply force the cable onto it.

Place the cable in the terminals and tighten then back in the plug.

You must have the correct cable in the correct terminal
The earth is always at the top (green and yellow stripey)

The live (brown) is always by the fuse.

The neutral (blue) is therefore the only terminal left

Make sure the terminals are tight and there is no bare wire showing.

Tighten up the strain relief so it clamps the outer insulation.

Screw the plug back together.

NB some plug types will be slightly different so you may need to alter the cable lengths and how much insulation you remove. The key is to get a good firm connection with no bare wire showing