You receive a message in your personal events when it is approved. How long it takes depends on how quickly two art team members have time to approve it. Could be a few hours or a few days or possibly longer if it's particularly controversial.
When you submit an image it doesn't apply it to anything. It just saves it to your art folder as it were. You then have to go back and apply it to one of your ships using its id, whereupon you can choose from any of your images and apply them.