Iron soup kettle with rust

I'm assuming that you're referring to a cast-iron kettle. One of the common strategies for removing rust from cast-iron is to rub the oxidized areas with steel wool. You'll want to remove as much of the rust as possible that way, and then you can consider using a wire or plastic brush, soap and water.

Subsequently, once you're confident you've removed the rust, brushing with food-grade flaxseed oil (or shortening, in a pinch) and heating the pot for a period of time, then letting it cool so that the coating is mostly polymerized, will help reduce the likelihood of future rust development.

There is a guide to restoring cast-iron covering roughly the same set of steps.

The reason for preferring flaxseed oil is its polymerization properties as noted above, but you may want to see a more detailed explanation.

If it's cast iron or steel (definitely don't do with aluminum, stainless, or galvanneal), then the best and coolest way is to remove rust with electrolysis.

You can look up tons of videos on YouTube, but at it's simplest, you take a Rubbermaid container, filled with tap water, add a portion of washing soda (easily found at walmart), and suspend the item you want the rust removed from in the solution. typically by a stick laid across the top of the container.

To make it work, you put sacrificial metal inside the water/washing soda solution and around the perimeter of the container. Then you take an old car charger set to the lowest amp setting and clipping the negative clamp to your item you want the rust removed from and the positive to the sacrificial metal. Of course you have it unplugged while doing this. Plug it in and watch it work. I forget with is the cathode and which is the anode, but the rust gets stripped from the object and attaches itself to the sacrifice metal. The sacrifice metal ends up looking like some barnacle encrusted piece of junk.

You need to read up on doing it before you try it. Every video goes into how it works and why. They usually contain safety info as well and you need to pay special attention to it. It's one of things where it's easy and safe, but you can get yourself in trouble if you ignore some basic safety precautions. Most things are like that though. There are precautions to take, but don't get scared off of it. They actually use this method to keep a battle ship somewhere on the east coast from deteriorating. The salt water it's sitting in is a great conductor, which is what the washing soda does by the way. They drive in large steel posts around the ship and replace them periodically.

I'll hit the safety big ones. Firstly, this process give off a flammable gas. From every story I've heard, it hasn't every harmed anyone when ignited, it simply blows nasty, rust foam all over their shed, and it it's because they were doing it in a small enclosed space that it could build up enough to ignite in the first place. I've never heard of it happening when done outside.

The second big no-no is using anything but steel in the solution. Stainless gives off hexavalent chromate which is toxic to breath and galvaneal and galvanized give off bad gas as well. You shouldn't use aluminum, but only because it easily pits. What this process does is remove a very fine layer of metal at a time and it seems to work extrememly easily on aluminum. You can try it, but could damage the finish. If you stick to regular metal or cast iron, though, everything is cool. You can even reuse the water multiple times and pour it out on your lawn when you're done. Nothing toxic to it. And if you turn the car battery charger on a low amp, there isn't an electric shock risk either. I wouldn't stick my hand it in, but it isn't going to zap you if you do.

Here is an instructables link: http://www.instructables.com/id/Electrolytic-Rust-Removal-aka-Magic/step4/Attach-charger/#intro