In more recent days, one could also get what is referred to as a hosted AdSense account via Google services like Blogger or Youtube, and for Blogger, get to display the ads via a Blogger AdSense gadget (Dashboard > Layout > Add a gadget > Add an AdSense gadget).
However, recently bloggers had been reporting problems adding an AdSense link unit this way. What the blogger can do is to apply for a regular AdSense account. Or if you have AdSense ads via other host parner but want to display ads in your non-host partner website, you should also apply for a regular AdSense account. Here is how:
1. Sign in to your AdSense account.
2. On the Home tab, visit the Account settings page.
3, In the "Access and authorization" section, next to "Only host sites are allowed to show ads for your account," click edit.
4, On the “Show ads on other websites” page that appears, enter the URL of the site where you plan to show ads.
5, Click Submit.
6, Finally you need to implement AdSense ad code on the URL that you provided above, on a page that receives traffic.