If your bicycle is rusty, an easy way to get rid of surface rust is to pour lime juice on a piece of steel wool and scrub the rusty areas. The citric acid in the juice will react with the iron oxide (rust) and make the rust easier to remove with an abrasive.
This trick works for tire rims, gears, and other rusty bicycle components. However, using it on the chain is a little risky. If you properly clean off the acid (by rinsing and drying thoroughly), it should be fine, but remnant acid could weaken the chain. So be careful!
Instructables user joshf discovered this method from a book on Japanese life hacking techniques. (Urawaza) Although the author uses lime juice and steel wool any combination of citric acid and abrasive should work similarly well.
When you’re finished removing rust, make sure you remove all of the lime juice to prevent any leftover citric acid from weakening the metal. For full photos and the author’s technique check out Remove Rust from a Bicycle with Lime Juice.