The first thing you need to do is to turn off the water supply to the taps. Most modern plumbing feature a isolator valve on the pipes close to the taps which can be closed with a screwdriver. If your pipes do not feature an isolator valve, turn of the water at the mains stopcock and open the taps to drain the system.
Disconnect the pipe connections beneath the taps and then unscrew the backnut which secures the taps to the bath or sink with an adjustable wrench. Lift the old taps out of their holes and clean the area around the holes to remove any built up dirt, rust or soap scum.
The distance between the holes on a standard bath or sink is about 180mm, and if you are exchanging single taps for a mixer unit you need to check that the tap fixtures are the correct width to fit (of course, this should be checked before you buy your new mixer unit). slot the new taps or mixer into the holes, making sure the rubber or plastic sealing washers are in place to prevent leaks. Fit and tighten the backnuts to secure the taps into place and then reconnect the pipes.
If the existing pipework does not quite match up to the connectors on the new taps, you can buy flexible pipe connectors to join them up. Flexible pipe connectors come in a range of lengths, but you will nearly always need to trim the existing copper pipes to fit them. Copper pipes can be cut with a hacksaw or a chain pipe cutter if you have enough access. Make sure you file the newly cut end of the pipe before fitting the flexible connectors. Once these are tightly fitted to the pipework, connect the other end to the taps.
Release the isolator valves or turn the stopcock back on and run the taps to check for leaks before you replace the bath surround.