The Advertising Manager plugin is the successor to AdSense Manager. As its recent name change already suggests, it supports a lot more advertisement networks than Google AdSense.
Installing the plugin starts with the download of the software package and uncompressing it in the plugins/ directory:
cd wordpress/wp-content/plugins/ unzip ~/advertising-manager-xxx.zip
Now go to the Dashboard -> Plugins section to enable the new Advertising Manager plugin.
You now have an new Ads menu entry in the Dashboard. After clicking Add New, you can directly enter the code snippets to include the advertisements. These parts are provided by your ad network.
For example, if you have a Google AdSense account, you log in and go to AdSense -> AdSense Setup -> Get Ads.
After you have entered the code snippets for the formats you are planning to use, you go to Dashboard -> Appearance -> Widgets. There you can drag the Advertisement widget onto the Widget Area where you would like the ad to appear.
As you can see, we placed a wide skyscraper on the right (in the Secondary Widget Area) and a (image-only) leaderboard at the bottom (in the First Footer Widget Area).
Do not worry when your advertisement is not displayed immediately; Google AdSense takes a little time before the ad is available.