You call Disney CRO and make a reservation for this service. Then (hopefully at some point!!!) they will send you special luggage tags (2 per person) that you will place on your checked luggage at your home airport. Then, when you arrive in Orlando (MCO) you go to the meet and greet area for DME where you will board a bus to your resort. Meanwhile, your bags will be taken directly from the plane area to a truck and then to your resort. You will see it again when you check in at your resort.
For your return trip, when you check-out of your resort, you leave your bags with bell services and play until it's time to leave via the bus. Then, you and your luggage hop on the bus and back to the airport you go.
Now, if you are flying on one of the participating airlines, we are on Song and it is one of them, you are able to actually 'check-in' for your flight at the resort front desk area. Your bags are then taken to MCO on a special truck. When it is time for you to leave, you hop on the DME bus, go to the airport and head right for the security area since you have already 'checked-in' back at the resort.
And it's all free...well, at least for 18 months or so. It seems they are having some issues at the moment getting it started but hopefully, within a few weeks it should all be fine.