Once you have your BoG ADR for lunch, you can go into your
MDE and next to the reservation, there should be an option to pre-order. Click on that and the menu pops up, and you can choose what you like and add it to your cart. You don't pay until you are seated and have received your food at the castle though, and you can make changes at any time beforehand until the moment you check in at the castle entrance. Keep in mind there is no AP discount for BoG lunch (we found out at the time since we didn't know).
Mobile ordering only works at a couple select restaurant throughout the 4 parks. As long as you have a cc on file in your MDE, you can pre-order and pay for your meal, and once you are in range of the restaurant, you can click I'm here, and in a few minutes they will let you know your order is ready and you just walk up to the mobile ordering window and grab it and go. We walked past at least 15-25 people waiting in the regular line every time we used it, they all looked at us like "what the heck??? How are they getting their food already?". Saves a TON of time if it is busy, since a lot of people apparently don't know about it yet. You can't get AP discounts or use the dining plan with that yet either, so that might be why it isn't popular yet.