AdSense registration page - click to enlarge.
Google has made it easier than ever to register for AdSense - simply head for the AdSense home page (https://www.google.com/adsense) and click on the 'Click Here To Apply' button. You'll then be confronted with a registration form to complete (shown above). The AdSense team will then review your site, check it complies with the AdSense terms and conditions before sending you an email accepting/rejecting you. It usually take a couple of days to hear a reply. It is very important you have fully read, understood and intend to abide by the terms and conditions.