First of all you need to make sure what type of tap you require
Mono block A mono block tap will fit a 1 tap hole basin only, these usually come with a pop up waste kit Inc with the tap unless otherwise stated or are imported! Make sure..
Standard taps pair All standard taps 1 tap for hot and 1 tap for cold will fit a 2 tap hole basin, they will have 1/2 inch inlet at the end of the tap and normally have washers that you will need to replace in years to come.
Ceramic disc taps pair All ceramic disc taps 1 tap for hot and 1 tap for cold will fit a 2 tap hole basin, they will have 1/2 inch inlet at the end of the tap. This type of tap has ceramic discs instead of washers. They will only require a quarter turn to turn the m on and off.
All basins will have either 1 or 2 tap holes, so make sure you get the right tap for the job.
First, check under the basin for the pipes and look for isolation valves, these valves usually have a little screw type head in the centre of the valve, turn the screw section until it runs horizontal to the pipe work.
Turn on the tap to make sure no water comes out the spout, then under the basin where the pipe work meets the bottom of the tap you will find 1/2 inch nuts that are attached to the tap, undo these nuts, this will detach the pipe work from the tap. Next job is to remove the old tap from the basin, you will need to look under the basin and locate the back nut, to undo this you will require a basin spanner, a funny looking tool that will get up into this tight spot. Trust me dont even attempt to undo this nut unless you have this tool, you will spent an hour on your back with arm ache and you will probably crack the basin. It is best if you can have someone to hand as these nuts are usually very tight, Get your friend to hold the tap while you are undoing this nut, so to stop it from spinning as you undo.
Once the tap is out, place the new tap in position, remembering to place the black flat washer that came with the tap over the 1/2 inch outlet so the tap is not just sitting on the basin, this helps in cushioning the tap on the basin. If the connection on the pipe work has a fibre washer, replace it now. Dont try to use the old one that is on there as you will find it will leek!. Reconnect the pipe work up to the tap giving the nut a hand tight plus about a 1/4 to 1/2 a turn with the basin spanner. Turn back on the isolation valve and if all is well new taps installed with no leeks. If the water connection nut has a little drip, just give it another 1/4 turn while your friend is holding the tap.