Looks like (from the way the fabric hangs) the neck is cut on bias (standard). Next piece is on the grain. Mid section is back on bias (look at the drag lines). Bottom (hem) is on grain, folded back.
Let's say that's a 1/4" piping. Cut the piping to 3/4", attach it to the pieces (on the edges), then fold them on each other, like a letter in an envelope. Then go over and press then sew down the middle. This seals your seams with a top stitch.
You're on your own for the sleeves. But, the sleeves look like they're all one piece, with the ribbon sewn on top for the look.