Wow. There is a serious lack of information in that article. I think they assume that anyone working on that project already knows how to finish a "quilt-as-you-go" project. I'm wondering if maybe it's part of a larger article that was published in the magazine, and the magazine gives you ALL the instructions - but it sure would be nice if they could state that somewhere.
If you want to make this, I would recommend googling "quilt as you go" or "cotton theory quilting" and you will find lots of information about this. A woman with the last name of Cotton (sorry, can't remember her first name) has written books about this subject, you may be able to find it at your library.
Or, you could make a string top and use traditional methods to quilt it. There is a good paper-piecing tutorial that uses the sew-n-flip method here:
http://www.filminthefridge.com/2009/...pieced-method/
And here is a tutorial I wrote that uses a different (and I think faster) technique than the sew-n-flip:
http://www.seamstobeyouandme.com/wor...uilt-tutorial/