As with fitting your light fixture (and any other electrical work) make sure the fuse box is shut off so there is no chance of you being electrocuted. Changing an outlet in the bathroom is very similar to changing any other outlets in the home except for you are around water. Water and electricity do not mix so you need to make sure the breaker switch (fuse box) is off. Take your test light and check the outlet after you shut the breaker off to ensure there is no power going to the outlet. After you have done this, it is time to start replacing the old power outlet.
The first thing you need to take off is the cover panel to the outlet. To remove this, a center screw usually holds it in place, unscrew this screw and the cover will come off. Once the cover is off you are able to see the other two screws that hold the outlet to the wall. Take the top and the bottom screw out to remove the actual outlet from the socket, now you should be able to see the electrical wires attached to the outlet. Remove the wires but make sure you know what side they go on when you are installing the new outlet.