Repairing RRoD:
RROD is a somewhat generic term as red lights come up for many errors, usually though it refers to hardware failure as follows. I do not really rate any one guide and many have incorrect info or blatant misinformation buried within them, only real way to get this is to read many guides.
Basic idea is that courtesy of lead free solder and a poorly supported motherboard (which leads to bending/warping of the board with the CPU/GPU taking much of it) the connections on the bottom of the CPU and/or GPU which use a form of connection known as ball grid array (as the name implies rather than pins to hold it on you have little ball of solder) either break, creep, bridge (whiskers) or otherwise become malformed.
Every fix you will see on the internet is a way to try and fix this, they range in quality and effectiveness but a rough overview could be:
Towel fix: do not do this ever, I mention it only so you do not do it. It overheads the entire 360 probably taking most of the electronics (or at least a good chunk of their lifetime) with it in an attempt to heat the CPU/GPU connections and get them to reform (remember solder is fairly easy to form at room temperature and the 70 something Celsius the 360 overheats at is good enough to start reforming.
Cent fix/penny fix. Varies slightly according to the guide you follow but generally you bind two or three pennies/cents together with electrical tape (to prevent electrical bridging) and stick them on the bottom of the RAM chips (sometimes three of them, sometimes all four of them). This redistributes the stress over the motherboard (aiming to entirely free it of them actually) and so helps with the connections.
It can work by itself (indeed I have done such a thing) but it is usually coupled with either the heatgun method or another method.
Similar methods have also been used with xclamp replacement and bolts and custom force redistribution methods.
Xclamp fix: varying kits here and probably all about as good as each other.
Similar idea to the cent fix above but instead of redistributing stresses over the motherboard it adds stress to the heatsink which pulls down on the chips hopefully fixing bad connections. Usually coupled with a heating fix.
Heatgun method.: Here you take a heat gun (electronics rather than paint stripper if you can, some buy their own and some make one from a powered desoldering iron and a pump which can create a stream of air) and heat the CPU and/or GPU up in an attempt to reform connections (some advocate a more general heating pattern, I am not convinced it does anything other than waste time), it is usually worth supporting the CPU/GPU at the time to prevent the self weight of the chips from "squashing" the solder beneath it and many also shield everything but the section they are heating with tin (aluminium) foil.
A major problem with this is popcorning where the chip case has water in it which turns to steam (expands) or the case otherwise expands too fast and fractures the surface (usually not bad in and of itself but it does a good job of destroying any heat transfer ability beyond the repair capability of most people.
Crude alternative: if the CPU overheats the 360 more or less stops but if the GPU overheats then all is good apparently. Turning the dual fans 90 degrees allows you to cool the CPU and allows the GPU to overheat and so fix connections (at least in theory).
BGA reworking: if you have played at all with modern electronics you will probably know about surface mounted devices. While still technically a surface mount technique I personally rate it as harder to play with than surface mount. Search youtube for BGA rework videos and know that the hardware to pull it off is quite costly (even if you do not buy the special stuff) and the skills to do it are a cut above normal soldering (especially if you are not going in for the good equipment) although you can net things from places like virtual village and ownta for the job. It is very much as case of if you have to ask you are not ready for it yet.
A video to get you started (not for the 360):
http://www.youtube.com/watch?v=YdN53F5YQwk&fmt=18
Every other fix method before this attempts to either achieve similar results or addresses a cause of the problems, as such this is the king of all methods but as I have hopefully made clear this is no simple feat.
Long story short it is entirely possible to fix most RRoD consoles and aside from BGA it is entirely possible for anyone for anyone who has basic reading ability.
