How do you get rid of the white buildup around the faucet of the bathroom sink?

Depending how much buildup you're talking about and exactly how it's built up, chip away at it with a razor tool ($3 at Lowes) or a regular razor scraper (link for if you don't know what to look for) -- blunt the edge first by rubbing a screwdriver along the edge so it's easier not to scratch the sink/faucet much. Start slow and just apply pressure and try to get UNDER that white stuff; don't try to cut through it or scratch at it. It will chip off in little bits as you get between it and the sink/faucet. Scrub at the remaining white stuff that you can't get under with a paste of CLR & Comet, using a scotch pad. Leave the paste on for a few hours, scrub, repeat until gone.

heat some white vinegar and soak a few paper towels or some sort of cotton cloth like a t-shirt or really long sock and wrap it around the part that needs to be cleaned. Allow to sit 10-20 minutes and wipe it away with whatever you soaked in vinegar. If you notice a stain from it being there so long, just grab a canister of BarKeepers Friend (in the cleaning aisle by the comet and ajax that never work) and make a bit of paste with it and some water, dip an old toothbrush in the paste and scrub that stain away. I used barkeepers friend to make my sinks, counter tops, tiles, grout and many other things in my home look almost new again. It deep cleans any surface without damaging it and it gets to stains that bleach wouldn't touch (kool-aid, blueberries, rust and others). Try it you'll love it.

Oooh, hard water!

You can use white vinegar to get rid of it. Pour the vinegar (do not dilute, use it straight) onto the surface and let it be for a while, minimum of ten minutes, then rinse. You can use some salt too if you need some abrasive action to help scrub it off. The salt will make it about as abrasive as Comet, so shouldn't damage your faucet.

I should say, your mileage may vary with this technique, different areas have different minerals in their water and what works for me may not work for you.

A pumice stone will scratch the surface. Have you tried vinegar on an eraser sponge? Sometimes using CLR on an old toothbrush and scrub away.

Usually chemical buildup. Get some "CLR" at Home Depot. Calcium,Lime, Rust Remover. I just used it last week on one of our drinking fountains. Works great!!!

if it's on the spout part of it take a sandwich bag and a rubber band pour lemon juice in the bag then wrap around faucet. let sit for several hours when you come back it will be gone.

CLR works pretty well but you need to keep it soaking for awhile. That is what I use.

Lime-away. Home Depot or Lowe's

Try a cream cleanser like jif mixed with some white vinegar, it is probably a calcium deposit.

Over here we get these wirey crubbing pads with some cind of cleaner in them.