First of all, choose the blog that you want to put AdSense on, and go to the Template | Page Elements tab. You can get there by clicking the Layout link on the dashboard, or clicking the Template tab from the posting or settings page of the blog.
Once you're there, click one of the Add a Page Element links. Choose the one that corresponds to the area of the page that you want to contain your AdSense ads. When the 'Choose a New Page Element' window comes up, select the AdSense option.
The next page displays an AdSense sign-up page. If you're new to AdSense, go ahead and fill it out to create an account. If you already have an AdSense account, click the sign in link instead so you don't accidentally make an extra account.
Once you've signed in or created or account, you'll get the configuration screen. Use the menus to select a format, and one of our preset color templates. If you want more control, you can also enter colors of your own choosing by typing the hex codes in the spaces provided.
If for any reason you need to switch to using a different AdSense account, click the Switch to a different publisher ID link at the bottom.
When you have things the way you want them, just save your changes and go see how it looks on your blog. Come back to tinker with the settings any time by clicking the edit link for the AdSense unit on the Page Elements tab.