If there's any water in your sink and you plan on taking off the U-bend, have something larger than a washing up bowl ready. I blocked my sink and even with a couple of inches of sink water it almost filled a bucket up.
Also, if you bung a kettle full of boiling water into the sink, leave it for a few minutes, then you can feel along the pipes to see where the 'hot' ends and there's your blockage.