How do I remove rust from pulls and knobs on a dresser?

You can try soaking them in apple cider vinegar for a couple of days. You will see the vinegar turn reallly dark when the rust starts dissolving. Another thing you can try is marine jelly, can purchase at any marine or boat store.

I use 0000 steel wool, and sometimes if really bad a fine soft brass wire brush.

I've read/heard that ketchup/or tomato sauce in Australia, can clean brass etc.. I used tomato sauce to clean 2 wine goblets (silver). They came up beautifully. I left the tom. sauce on for a while, washed, dried. Didn't even use a silver cloth (jeweller's cloth).xo

https://www.thespruce.com/how-to-refurbish-hardware-2878995

Remove the hardware, soak in a soapy water solution, use a wire brush to clean/scrape away rust, repaint with a metal paint in the colour of your choice

See if they will clean up with a fine steel wool.

I agree with using 0000 steel wool and a little vegetable oil rubbed on.

Remove the knobs and clean with vinegar and water. Lightly sand and clean. Let dry and then spray paint them to any color you want.

I know sounds a bit off but I think worth a try. Clean well and simply put them In a container you can throw away and fill the container with regular coca-cola. Leave them sit for a few days.

You may paint them.