Initially remove any obstacle
from in the plug hole i.e. food, hair and other blockages.
This can be achieved by using a suitable chemical cleaner
or caustic soda. (Ensure chemical is suitable for the type
of sink and plug hole you have e.g. enamel sink or chrome
plug hole).
If this does not clear the sink
then a sink plunger will be required.
Before 'plunging' cover the overflow
with a damp cloth and hold it there, this will force the
air to hopefully clear the blockage.
Place the plunger cup over the
plug hole, and plunge vigorously up and down for a minute
or two.
Should the plunging not clear the
blockage then the next step is to remove the trap under
the sink. A bucket should be placed under the trap to catch
the water, which will come from the sink.
Check the trap for any blockage,
if it is clear then a pipe cleaner (such as a flexible curtain
wire) should be used to dislodge the blockage if possible.
(See Clearing a blocked waste pipe)
If the pipe cleaner does not dislodge
the blockage then it is probably in the drain. (See Clearing
blocked drains)