It is really dependent. You get the first email in 6 to 8 hours then you have to put up the test ads, then you get another email that says if the accept you or not which is typically 2-3 days. Be sure your site is ready for Ads AND you have traffic, low impression numbers can hurt you.
Please read AdSense DOC's and learn the system
If you get approved make sure you do EVERYTHING in your power to not mess that account up and get it suspended. It is very difficult to unsuspend any Google account that get his with their suspensions.