How can I build a vanity around a bathroom sink in a very tight space?

Hi Lynda! Could you post a picture and some measurements?

Here are a few ideas. If you want a really cheap way... when I was in my studio apartment I just had a little sink in the bathroom, no storage. I got to small plastic baskets, some pretty fabric and Velcro. Put the two baskets on the floor under the sink then with the self sticking velcro, I went around the sink and on the fabric. Then stuck the two together. That way, when I moved out I just peeled it all off.

https://www.hunker.com/13404059/how-to-build-a-vanity-around-a-pedestal-sink

https://www.homedit.com/diy-bathroom-vanity/

IKEA has a set of 5 stacking legged baskets for $10, that can be stacked with any number you wish.

Its soft enough to drill small holes and fasten a small curtain rod for a simple fabric panel to cover the contents.

Take measurements of the space available, keeping in mind things like leg room when using the potty and the doors that need to open and close. Look up Ana White on building cabinets and then build one that will fit your space. Basically, a cabinet is a wooden box with bits that open, so as long as you have reasonably good amateur carpentry skills, you should be fine.