What does it cost me ?
Nothing, the program is free.
Do I have to live in the USA to join ?
No
What should I have before I apply for adsense ?
A working website or blog, not one that is under construction, good content, lets say if I search for how to paint a car, I want to get info on how to do just that and not go off on ten other things with little info and a lot of ads, have at least three to five good articles and some useful links, If you only have one page right now with good content that should be ok, If you get turned down add some pages with content and apply again, remember to try to stick to one topic, that way when google scans your page the ads will be relevant to your site topic.
What's the easiest way to begin?
Creating a simple blog.
