If you know there is something stuck in your line, use a plunger to try and dislodge it. The best tool for this job, however, is a plumbing snake, which can rid your lines of most clogs with relative ease.
You will need to insert the cable into the clean-out, then feed it down through your line until you feel it drop into the main drain. Then crank the handle to send the cable further down. When it gets near where you know there's a clog, turn the handle clockwise again to back up any debris that is loose in your line. You should be able to pull out some nasty stuff this way.
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