What should I learn first?
I have a guitar around the house but no one here plays so I have no one to teach me. No money for lessons.
How can I learn the guitar on my own?
I would learn how to read tablature (tabs) http://guitar.about.com/od/tabchordslyrics/ss/read_guitar_tab.htm and the finger shapes of the more common major/minor chords like C, D, A, E, G and Em. There are a number of online guitar courses available that cost money but only what you would pay to get 2 or 3 lessons from a real teacher. I own Jamorama (about $40) and Learn and Master Guitar (about $150 I think). They are both excellent courses and use videos to teach. http://www.stampproject.com/guitar.htm
If you can’t afford Jamorama, then I suggest checking on Youtube for Justin Sandercoe. He provides some great lessons for free and is a pretty good teacher. http://www.youtube.com/user/justinsandercoe?blend=2&ob=4
For your first song with strumming and chords, I suggest learning Pearl Jam – Last Kiss. The chord progression follows G – Em – C – D with simple up and down strumming. And for songs where you are picking (plucking strings individually), I would suggest simple songs like Old McDonald, Twinkle Twinkle and Happy Birthday. Ok… so that is a bit lame, but it will help you learn some of the basics.
Good luck with learning to play. And remember, it is starting that is the hardest. Your fingers will get sore until you develop some tougher skin on the fingers, but hang in there and keep practicing.