You first get a list of blogs you are following and click on add a blog. You can add any blog and not just those on the blogger platform (like wordpress.com integrated reader)
You then enter the blog by url. There are extensions to chrome that add these in one step.
You then can choose to follow the blog publicly or anonymously
Tou can then add a widget on any page.
You then select to add blogs by url or add them from your following list
The latest posts from blogs I follow are then added to my site. You can change the settings to only display urls and names, snippets, or feature images.