I would probably machine wash it in cold water, and then lay it out flat on a towel on top of a waterproof surface--like a countertop or something. I usually stretch the object some so that it's the proper (or original) shape, and then just let it air dry. Some people pin the garment or object down if they think it's going to shrink, but you probably don't need to do that. However, after leaving it overnight, you may need to flip it over once, making sure it's still shaped correctly, and let the other side dry.
When it's completely dry, you can add your lining and snaps. Final instructions: Take another picture or two and post it on KH for us to oooh! and aaaaah! over!