pawel mentioned a good site. There are many other sites out there ... and a number of good books as well. Read up on all you can find.
Cost could be anywhere from reasonable to outrageous, depending on how ambitious you are and how carried away you get. Don't build a guitar as an attempt at saving money. You can always find the same quality for less money than what you could build. The reason to build yourself is 1) for the satisfaction, 2) no better way to learn about your guitar and how to set it up and maintain it 3) to do something "custom", to give yourself exactly the guitar you want and that is truly unique to you. (custom paint, pickups, neck, inlays, body shape, etc...)
I finished my first custom a couple of years ago and I have to agree with everything said here so far.
A friend of mine who helped me out alot gave me some really good advice. Basically, dont look at a project like this as something that you have to get finished quickly, or even to a deadline. It will take at least 6 months, and there will be stresses and disappointments on the way. Suppliers will let you down, parts will be tricky to get: you must keep the faith through all of this.
I was really just getting parts and bolting together, with little or no actual construction. I ended up changing everything, buying a new (blank and unrouted) body, and starting from scratch half way through the project. Very expensive and frustrating. Another friend of mine was doing the finishing on it, and took longer than expected (which is fair enough as he has a life as well). I was so stressed by this point that I didn't allow enough time for the lacquer to harden, and it ended up getting chipped and all sorts. Stupid me.
However when I first collected the guitar, finished and set up, and actually played it I was so happy that I almost forgot all the other trials and tribulations. It is still my favourite guitar (along with my Jem of course), and I can't wait to perfect the design next time.
As far as cost goes, I spent £800ish on the finished guitar. Which for an Alder bodied reverse headstock strat, in flourescent pink, with a schaller floyd, and dimarzio pu's I think that's pretty good value. Further to that I learnt an awful lot. I probably wouldn't spend £1000 on another "guitar off the shelf", but I would spend that building another custom, probably to perfect the design on the pink strat.