Disconnecting the water and waste
Switch off the water supply. Open the taps to drain any excess water.
Disconnect the waste trap, keeping a bucket underneath to catch the water.
Undo the hot and cold feed. How you do this will depend on whether you are replacing like for like, or whether the new sink requires adjustment of the pipes. Either undo the supply pipe connections at the base of the tap or cut the pipe with a small hacksaw.
Replacing sink taps
If you wish to replace only the taps, disconnect the existing ones where they join the supply. There are several models of tap spanner available to make this job a little easier. As you have probably discovered, the connections for these (as with many other plumbing connections) are a little awkward to get to. The tap spanner is devised so that the head is mounted at right angles to the shaft. This enables leverage to be made from an oblique angle. There are even self-gripping multi-fit multi-angle tap spanners.
Remove the sink
Undo the sink fixings and remove from the worktop or cupboard.