There are a lot of tutorials out there for seasoning your cast iron, but not a lot about getting rust off. (One I found involved oven cleaner. NO thank you.) The ones I did find used steel wool, which I didn't have handy and I don't much care for it anyway because I always manage to cut or scratch myself with it. So...I used what I had sitting around and got to it.
What You Need
The end chunk of a potato (enough to be able to hold firmly)
A rusty cast iron skillet
A little vegetable oil (canola or olive will do)
Gloves (optional, but recommended)
1. Place your rusty skillet in the sink and sprinkle a couple tablespoons of salt into it.
2. Take your chunk of potato and start scrubbing. The moisture from the potato will be enough to help the salt dig in to the rust.
3. The salt will get dirty very quickly. You may choose to rinse out the pan to survey your progress. If there is still rust, add more salt and repeat Step 2.
4. Continue to the sides, edges, bottom and handle of your pan.
5. Rinse thoroughly and pat dry.
6. Place pan on stove burner, this will help dry any remaining moisture.
7. Once dry, put a small amount of vegetable oil in the pan and rub it in with a paper towel.
8. Keep pan over low heat for at least 30 minutes.
9. Let skillet cool. Make sure to wipe off any excess oil before storing your skillet. If you leave extra oil in the pan it can turn rancid.
10. Every time you use your pan, after you've cleaned it (I never use soap, but that's up to you), put the pan on a low burner and repeat the oil and paper towel step. It's best to store your pan in the oven, but it worked much better when stoves had pilot lights that stayed on (thus keeping ambient moisture away from your pans).
Additional Notes: As I said above, I never use soap on my cast iron pans. My dad's way of cleaning was to wipe it out with a paper towel when it was still hot and then run it under some water (if needed), then put it on the stove with a bit of oil to reseason it. Many people do just fine using a mild soap and sponge, but I urge you NOT to scrub it with soap. That action will break down the seasoning you've worked so hard for. You don't want to start from scratch each time you use your pan. It would become a miserable experience and you'll hate your cast iron.