This is a pretty critical skill if you're working on a car that's not brand-spankin'-new, and very critical if you're working on a ten-year-old rustbucket. Every stuck fastener is a little different, but these guidelines should help a lot.
1) Get a good tool on it. 6pt sockets are much better than 12 pt, and a box-end wrench or a socket is better than an open-end wrench. Vice grips are okay sometimes, but are at the bottom of the list with adjustable wrenches and slip-joint pliers. Many times a snug socket and good long ratchet will break very stubborn bolts.
2) Use leverage, but don't round it! Go ahead and throw a pipe on the ratchet/wrench, but be careful - once you strip the head, you're in a world of hurt. Air tools often are less likely to strip in many cases, but they also dont' usually give as much warning - I prefer to break it loose with a wrench first, if at all possible. A normal drill/driver won't break stuff loose, but it can help wind out long bolts. I use one all the time - it's much better than cranking a ratchet 1/12th of a turn 100 times.
3) Fight rust with fire. If you feel like you're not going to get it without possible tool/fastenera damage, torch the sucker! Propane works well, MAPP gas is better, oxy-acetelene is best. If you don't have a torch, get a MAPP or propane job. You really do need one. Be careful to position the flame so you're not heating anything rubber or otherwise able to be damaged by the heat. I have a couple pieces of flat steel 3/16" thick that I use as heat shields when working around brake lines, CV boots, and bodywork. Once the area is safe, hold the flame to the fastener and get it hot - 30 to 60 seconds is good with propane; you can get them red-hot in ten seconds with a cutting torch. The bigger the part and the more metal around it, the longer it'll take. After it's hot, give it a little bit to cool and then try your wrench again. Usually it will come off pretty easily.
4) Penetrating oil works a little. If you can't use a torch for some reason - you couldn't smuggle one into the junkyard, there's rubber too close, etc., give it a shot. But really, torches are so much easier and faster, there's no reason to screw with the oil otherwise. WD-40 is garbage for this - use PB Blaster or Liquid Wrench.
5) Smack the thing. If heat didn't do it, try knocking it around a little - sometimes they like it. A hammer blow to the fastener (using a punch if needed to reach) will sometimes knock it loose.
6) You idiot! If you stripped it or it's so rusted there's nothing to grip, you need to get creative. With the T-47 Torx bits on the Contour rear brake brackets, I use Vice-Grips. They have a big head with lots of room for the Vice-Grips, and a crappy torx stamping that rusts out and strips easily. When using Vice-Grips, be sure to get it nice and square, and REALLY tight. You want the teeth biting into the fastener.
If it's stripped just a bit, try a smaller size. It's often possible to get a metric/SAE tool that's just a little smaller than the fastener, and you can pound a it onto the bolt/nut and get a good grip. 12-pt sockets tend to break if you try this. You can also grind/file new flats onto a bolt that fit a smaller socket.
If there's nothing to grap with the pliers or socket, try welding something onto it. I keep junky old sockets and broken extensions around for this reason. Just weld it on and then you have something to grip. At this point the fastener is toast anyway. This works well for stripped security lug bolts/nuts - or ones you don't have a key for. This will get it nice and hot too, like the torch. I guess if you somehow have a TIG and no gas torch you could even heat a bolt with that. I have yet to end up in that situation, though.
7) You got it! If it's buggered, replace it. If the head is okay, but the threads are hurting, chase them with a tap and die. In any case, put some anti-sieze on the sucker before re-installing. It'll prevent rust and ease removal next time. You'll thank yourself the next time!
Chime in with your tips and tricks, guys. I'm sure I forgot something.
'95 Contour [71 STS | Track Whore]
'97 Miata [71 ES | Boulevard Pimp]
2006 autocross results