Ok, I will offer up my advice, based on 30 years of collecting and having either made, or at least seen, about every mistake in the book at some point.
1) Don't take them apart. It is a natural instinct that if something needs cleaned you want to take it apart in order to do a thorough job. However, more damage is done to guns when people that don't know what they are doing take them apart than just about anything else that ever happens to them. It isn't necessary to take them apart to clean them, it is more work to do it that way anyway, and you will almost certainly bugger a screw at best, or break something at worst.
2) Rust is removed with some kind of oil and some sort of abrasive. The gentler the better. Someone mentioned Ballistol up thread, I have always used WD-40, they are both mostly made of mineral oils. You can also find straight mineral oil in a grocery or pharmacy. I use a Q-tip to apply it to the area of metal that has rust. Try not to get it on the wood, wipe it off immediately if you do. I use small wooden sticks to scrape the rust off, toothpicks will work just fine. You only want to remove any red or loose rust, there is no need to clean it down to the bare metal. In fact, in my opinion, it is a major mistake to do so. The brown coating left behind by oxidation is referred to as patina, and it is what you want. Occasionally the rust is so heavy that I use things stronger than a toothpick, but without seeing photos I hate to say anything about that. It is a judgement call based on years of experience. Once the loose rust is removed I like to coat the metal in grease, I typically use Hoppe's gun grease, and let it sit overnight. Wipe it off with a paper towel the next day, and you are done. I don't know if that last step is really necessary, but I have found that if I do this I don't get recurring rust. There are more expensive options like conservator's waxes that are probably better, but I have never used them.
3) The wood is cleaned like you would a fine piece of furniture. You didn't mention anything about the wood needing cleaned, so I assume it doesn't need any attention. Beginners do more damage to wood than can be believed, so doing nothing is perfectly fine and likely the best option.