I, like many aspiring rock stars, had to pay for all of my equipment. While all my friends were getting mommy and daddy to buy them $400 strats, I had to settle for a $40 electric I got from a video rental company. I didn't have enough for an obscenely expensive lefty, so I figured I would just play it backwards. Horrible, horrible idea. While it works for some players like Seal and Jimmy Haslip, figuring out chords like that almost turned me dyslexic. Little did I know how easy it is to switch a rightie to lefty.
The first obstacle a person restringing a guitar comes into is the bridge. In a strat style the low E might not fit through the high E's notch in the bridge. If possible, force it through the bridge. If not, take it into a shop to be proffessionally done. A proffessional job will run you between $20 and $50 depending on the store. Once you get the low E through the bridge string run it along the body like you normally would. Once it gets to the nut lay it across the itty bitty hole where the high E should be. Then put it in the string post of the tuning machine like you normally would.
On a strat-style guitar this system actually provides a better-playing guitar for drop-D or other drop tunings. The extra 3 or 4 inches the low E has to go increases the tension on the string and makes it less floppy. Be careful when winding the string. It is very easy for the low E and sometimes the A to pop out all of a sudden from their nut slots. It might be beneficial to use one hand to keep the string in place and use the other to wind until you get close to pitch. Miraculously, once the string gets tuned to pitch your worries are over. You can play as hard as you want and the string will not budge from the nut as long as you keep it in relative tune.
Repeat the process for the other strings, which should all be pretty easy except for the high E. The problem with the high E is that once it gets into the string post it has a ton of extra string because it is usually at the end of the headstock. It also has a lot more room in the nut than it is supposed to have. Paul McCartney used to cut up toothpicks and stuff the extra space with those. I do not reccommend this, as there really aren't many problems with the high E left in the low E slot.
The next conversion takes a bit more gusto and daring. Unscrew the screw holding the strap pin closest to the neck. Approximate the middle of the horn on what used to be the bass side and is now the treble side. With a hammer make a hole almost exactly on the other side from where th old hole is. Then screw the strap pin in and you're done!
The final modification is a lot trickier. No matter what kind of guitar you turn into a lefty it will have intonation problems once you're finished. Intonation has to do with the string's distance between the nut and bridge, and needs to be redone. I took it to a proffessional, as intonation is a very easy thing to screw up. If you're going to do it yourself, tune the guitar first. Then check the tuning of the 12th fret and then the 12th fret harmonic. They should be the same note, and if they're not you need to adjust the screw at the bridge and do it again until they are the same note.