This hip trick comes to us courtesy of my partner, who cleaned rust off her bike wheel rims and frame with this fun little science experiment.  
 
Try it sometime by pouring a couple cups of water into a bowl. Take a square of aluminum foil, dip one side into the water bowl and then rub the rust-affected area with the dampened foil. The foil will likely disintegrate after a while of rubbing, but if necessary, grab another square and keep at it until all rust is gone.

Shine chrome by sprinkling Kosher salt over a half of a lemon. Rub the rusted area with the salted lemon and then follow up by cleaning normally. Enjoy the shine!