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 basin requires a realignment of the pipes. Either undo the supply pipe connections at the base of the tap using a tap spanner which will provide leverage in this confined space, or cut the pipe with a small hacksaw.
Undo the basin fixings and remove them from the wall.