It's a long process if you live in the US and have no access to Arabic speakers. Even with access, it will take a while.
If you really want to give it a go, I suggest this book as a starting point. It's a good book to get started with the alphabet and some words and simple phrases. There is also a follow-up in the series that can take you a bit further.
http://www.amazon.com/exec/obidos/tg/detail/-/087840273X/qid=1089144477/sr=1-39/ref=sr_1_39/103-6860236-9155012?v=glance&s=books
Another good way is to read little kids beginning readers :) That helped me because the print was bigger. Also I really helped my reading skills by reading the signs in Cairo while stuck in traffic. I made a game out of reading a sign before I had driven past it :)