Ideas on how to wear this shift dress?

You could wear a cute little cardigan over it, and pair it with a pretty necklace and flats/sandals.

You could also wear a long-sleeved black & white striped tee underneath it.
 
You could throw a b/f blazer over it, a cardi, etc. and add accessories... necklaces, bracelets, etc. (whatever you prefer). Sandals or wedges are great "dress down" shoes too.
 
Personally, I don't like materials like polyester and rayon because they don't breath well in hot weather. And it may also be too hot to layer. But wear it with fun day shoes like flat gladiator sandals, espadrilles, or wedges. And wear a small casual cross body camera, messenger, clutch, or vintage bag (http://www.shopbop.com/messenger-ba...524441863314.htm?fm=search-viewall-shopbysize) or bold wooden accessories. I think wood jewelry tends to be more casual.