How do I replace a GFI switch in the bathroom?

Sorry, but what is a GFI switch? Do you mean a GFI receptacle that has the Test and Reset buttons on the face? Most likely this is what you mean.

Read the instructions that come with your new GFI before proceeding.
Shut off the breaker or fuse for this circuit/receptacle.
Test the receptacle to be sure the power is off before proceeding.
Remove the finish plate, usually two small screws
Remove the GFI device, usually two small screws.
Pull the device out gently, this will stretch out the wires connected to the back of the device, anywheres from 2-5 wires can be connected to it.
Note the back of the device, there are two terminals labeled Line, and two labeled Load.
DO NOT DISCONNECT ANY Wires, until you are sure which wire connects to which terminal.
Blacks(hot) or possibly another color other than white, will connect to brass screws, and white(Neutral), will connect to silver terminals.
Green or bare wires will connect to a green screw.
If there is only two wires, black and white, black will connect to LINE brass, white to LINE silver.
If there is 3 wires, the third should be the ground, which is green or bare and connect to the green screw.
If there are two more blacks/whites, they will most likely be connected to the LOAD,black-brass and white-silver.
Do not get any LINE and LOAD wires mixed up, otherwise there will be problems.
Read the instructions how to connect wires to your new device.Some use the type that want the wires wrapped clockwise around the screws. MOST use stripping the wires about 1/2", and inserting straight into the terminals under small plates under the screw head, and simply tightening the screw to squeeze the wire.
Gently fold and push the wires back into the box, making sure the wires do not get crushed or pinched, and pushing the device into the box all at the same time, until it is flush with the wall surface.
Install the two mounting screws, and the finish plate.
Restore power to the circuit/receptacle.
Test the GFI by using the TEST button, if it trips , reset it.
If it does not trip, then something is wrong,breaker is off or tripped, wires connected incorrectly, or a defective device.
Try an appliance or a lamp to be sure the outlet works.
Done.