I want my posts to have a featured-image thumbnail beside it, how do I do this?
First you may need to add featured image support to your theme, if that functionality isn't already enabled. To enable featured image support for your theme, add the following line of code to your themes functions.php file:
Next you want to open up the template that displays your post. Open up your single.php(or other) template file, and add the following code to check if the post has a featured image set, and if so, display it. I'll leave it up to you to figure out where and how you want the image to display.
(Cut/pasted from the OP.)
As it turns out, this is very simple.
Go to your Dashboard --> Genesis --> Theme Settings
Now in the box labelled "Content Archives" select "Display Post Excerpts" from the drop down menu. Now make sure the "Include the Featured Image" box is checked and select your image size.
The featured-image thumbnail will now appear next to your posts.