Great question. Metalworking is a hobby, but as a professional bottom-feeding tool junkie I can honestly say rust is my addiction. (I actually have a website with rust in the title.)
I've used electrolysis powered by everything from an old phone charger up to a car-battery charger. My additive of choice is baking soda, but others use some sort of powder found in the detergent aisle. All you need is a tub big enough to hold the part and an old piece of iron for a sacrificial anode. Plenty of online tutorials for that way, including some videos. You can plug it in in the evening and check in the morning, it seems to go faster with hot-water to start, the amount of soda isn't really that important - some tutorials say to put 1-2 spoonfulls in, but I just pour a bunch in and swish it around to dissolve. It only kills the rust and a green pad will quickly take off the black residue.
I've also used citric acid, just drop in and let soak. Do it too long and you will etch your surface, but do it just right and it will eventually eat the rust away. Same goes for the molasses, coca-cola, vinegar and other food-based recipes. Some people swear by it, I wasn't overly impressed but maybe that's because I'd already seem rust bubbling away via electrolysis in a plastic tub.
And the last thing I've tried, and still do occasionally for very small parts, is Evapo-Rust. You just soak the part until the rust is gone. It leaves a dark residue that you then have to scrub off with a green pad, but Evapo-Rust can be dumped down the drain when you're done with it. You can also re-use it (refresh with a bit of water) until it turns into a dark thick goo and needs thrown away. You can buy it in small bottles at most of the auto-parts store and I hear that Harbor Fright has it too. It's cheaper to find the big gallon sized jugs online. If you're doing something big you can pour it on a spot and cover with saran wrap so it doesn't evaporate.
All of the solutions will clean the rust if you're patient, some will also etch the metal if overdone, none will reverse any damage already done - pits are pits and no rust-removal will fill them in.
Joe