Like everything up to this point (minus your personal time) AdSense is 100% free. So head on over to the Google AdSense home page.
Now simply fill out the fields provided and voila!
Google states that they can take anywhere from 2 days to a week for approval, but my experience was quite quick - a couple of hours. Google's AdSense Help Center does a great job of answering all frequently asked questions. Now that we have an account we'll be able to put the ads on our blog page!