Over the last week, I was working on this rusty Schwinn. I was able to remove most of the rust using various methods. First, I made a paste from Bar Keeper's Friend and water and applied it to the rims and spokes. after some scrubbing, I wiped it off with a rag and rinsed it with a solution of Dawn dish soap and water. I also tried CLR on the chain rings to remove most of the rust. As a last resort, I sanded off the really stubborn rust before using CLR and a Scotch Bright pad to remove the remaining rust and shine things up a little.
I cleaned the entire bike including the drive train, wheels, and tires using Scrubbing Bubbles before re-assembling the bike. Finally, after pumping up the tires, I gave the entire bike a wipe down with wax trying to avoid the rims. Here are some before and after photographs.
Before:
After: