I know that this is not a crafty project as such, but I though it fairly relevant, and still a 'project' as such :)
I'm no guitar expert (I'm not even very good) but these are the steps I've taken to teach myself guitar, without paying for lessons, or buying those stupid teach-yourself books. This how-to is at least a start :)
The very first thing, I suppose would be to get a guitar. You can buy new one, a second-hand one, or steal it from your grandma's house, like I did.
(You could even buy a ukulele, which is smaller, cheaper, lighter, and easier to play.)
Next, make sure your guitar is in tune. There are plenty of videos on youtube explaining how to do this, so just search and you will find :)
I'd start off learning tabs from sites like ultimateguitar.com; doing this first will help your fingers learn the shape of your guitar, the frets, and get you used to wiggling them around in a certain way.
Each 'line' if you like, represents a string, and the numbers refer to wich fret to plonk your fingers in.
It's pretty simple to understand, but the hardest thing is getting your fingers to move in the right places at the right times. As ever, practise makes perfect.
The next thing you could do, is to make your very own chord chart. You can find various ones on the internet, but they're not always exactly what you want, and besides, copying out the tables will help you learn.
Practise each chord, starting with the simple ones (A, C, D, etc) and getting harder as you get better.
Next, find the chords for a song you know and like. Print it out or copy it onto paper.
Go through each line, slowly getting used to the changes between chords and such. With practise, you'll soon be belting out tunes.
("I'm a Believer" is one of my favourites, and the chords are pretty simple- a steady starter)