It's a manual process as far as I'm aware. Google employees will look over your site to check that everything meets their standards. They also look at their servers to see how it stacks up in terms of quality.
Ofcourse its manual process the google employees decide if your website is acceptable for terms of service or not
1. Apply for Adsense with url of your site - it would take them from a week upto a month to reply you 2. If you get approved, follow the policies of adsense and start placing ads
Adsense approval is a manual process. Make sure your website is compliant with Google policies before applying.