well i dont know what your plumbing skills are like, so before you try taking it apart at the u-bend try this
you remember as a kid in science class where you make those stupid volcanoes and fill them with vinegar and alka seltzer to make a "fun" explosion? well the same thing can work to unblock sinks.
just break up some alka seltzer tablets into the plughole, then pour in a ton of vinegar and it should start to fizz. if you leave it for a while, five minutes or so, then come back and rinse with hot water it might shift the blockage.
if that dont sound like its gonna work then you are going to need to get out your toolbelt and remove the u-bend and take out the blockage by hand.
