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Hi Vicki, it's pretty easy to do and as long as you prep it correctly and choose the right kind of paint it will last a long time. Here's a great video that will show you how to paint your own - https://www.youtube.com/watch?v=m9m1kBzOjhI
Here is some information to help you. https://homeguides.sfgate.com/paint-white-bathroom-sink-39595.html
there are kits to help you refinish your bathroom sinks and tubs. Find them at home improvement stores.
Lowes and Home Depot both have products that can help you paint your sink!
While you CAN, you shouldn't for long term care!
Here is how I painted mine: https://thehoneycombhome.com/transform-your-bathroom-with-sink-paint/
Do you mean the bottom cabinet or the porcelain top you don’t say.if it’s the bottom take the doors off and the knobs lay on news paper paint them with a roller so you don’t get brush marks roll sides of sink and bottom when dry put doors back on and get new knobs to dress it up. If you want to paint the bowl you will need to go to Home Depot for a paint kit for the sink.then just follow directions on your box.