from plumbingsupply.com (they say it is copper)
White vinegar is rightly touted as an excellent cleaning tool, and with the addition of salt, may be able to get rid of the blue/green stains. Try dissolving a tablespoon of salt in a cup of warm vinegar, soaking a rag with the solution, and letting it sit on the stain. The stain may begin to lift immediately - if not, try lightly scrubbing with the rag, and repeat the process if necessary. Because vinegar is a relatively weak acid and the salt is dissolved, this should be safe for any fixture material.
Another relatively safe option for most materials is to use lemon juice (or vinegar) and cream of tartar to create a mildly acidic paste that may also lift copper stains with some light scrubbing. Going up a level, you can also try using an ammonia and water solution (following the manufacturer's dilution guidelines) along with a bit of dish soap. Baking soda can be used as a mild abrasive to help with stubborn stains. Scrub with a rag or non-abrasive sponge.
If these aren't doing the trick, some have seen success using toilet cleaners containing sodium bisulfate. Before using any cleaning solution - but particularly harsh chemical cleaners - we highly recommend a spot-check in an inconspicuous area of the fixture to make sure you aren't trading one blight for another.