Once you are done with all the customizations, your AdSense code is generated in the AdSense Code box. You just need to copy this code (which is in the form of a programming script) from the AdSense Code box and paste it in your website as per the guidelines from Google. Since Google allows only three ad units per page, you can add the code at more than one place in your html code.
The next step is to save your web page to the designated web server (as per the instructions from your web hosting service provider). Please note that Google AdSense program does not require you to send over your website’s html code to them; neither does it ask to load it onto their servers or do anything else with it. The addition of AdSense code to your website’s code is the only thing that you need to do. Separate procedures are available with Google for people who want to use AdSense Ads with their blogs (you can check these on Google’s website for AdSense program).
Now that everything is done and dusted, you need to wait for a few hours (might be lesser than that) before Google’s web crawlers find your web page or blog that has AdSense code on it and you start seeing AdSense Ads on your web page or blog. You might see some PSA (charitable Ads) initially (almost immediately) but these will soon get replaced with the AdSense Ads that will earn revenue for you. If the content on your website violates the AdSense program’s policies, you might keep seeing PSAs even after few hours. In all such cases (or if you find objectionable Ads that don’t go even after you have applied appropriate filters), you will need to contact Google who will sort out the problems for you.