The Genesis Framework is a very powerful tool to build great websites with WordPress. Many theme developers already build their customization on top of it. If you display ads from AdSense or other ad networks on your site, Genesis is also a great choice because it makes it simple to add and place the ad units in various positions without the need for additional coding.
The reason Genesis and AdSense work so great together are hooks. They are placeholders who allow you to target specific positions for any content, not only AdSense ads.
If you are interested in playing with hooks in WordPress and PHP then follow the tutorial I wrote for Smashing Magazine.
In case you are less tech-savviy or just want to get the job done quickly, the free Genesis Ads add-on for Advanced Ads makes use of that built-in technique and gives it an interface.
After you created an ad you head over to the Placements page and create a new Genesis placement choosing the placement type with the following image.
Next, choose any of the positions available in the placement options. You can find a list of them through the add-on page.
After saving the options, your ad should be already visible.
If your ad doesn’t show up then beside the common issues it might happen that the theme you chose does not make use of all the documented hooks that normally come with the framework. In that case, take a look at the other available placements in Advanced Ads.