To begin with, the first cozy phone case is a traditional envelope that's been turned on its edge, so that the flap is on the shorter side. In general, the case is made using two granny squares turned 45 degrees and stitched together, and the squares can't bee thick or too stiff to bend tightly. Beyond that, the sky's the limit in terms of creativity. Other closures, different than the button and loop pictured, are also possible.
The full article about this pattern is on naztazia.com blog:
More info about Wollbienchen's project on Ravelry.