You need to make a reservation for Disney's Magical Express.
A few weeks before you leave, you get an information packet in the mail, as well as special DME luggage tags. You put one such tag on each piece of luggage that you will check with the airline (the suitcases that you have them load under the airplane for you ... that's called checked luggage, as opposed to carry-on luggage).
On the day of your flight, go to your home airport and do everything just like normal. Since DME exists only in the Orlando area, don't ask ANYTHING about DME at your home airport ... they'll have no idea what you're talking about, and they don't need to.
WHen you land in Orlando, totally skip baggage claim and go right to the Disney Welcome Center. Check-in at the counter, and then you'll be shown to your bus queue. You get on a plush motorcoach that will have guests from up to 4 Disney resorts on it. You can take your carry-ons onto the bus with you, but if they're too big they'll have to go under the bus (you can have the driver load them under the bus even if they're small and you just don't want to handle them).
You get to your resort, and the driver will unload any carry-ons you had stowed under the bus; if the driver handled any of your bags, a tip is customary. You go check-in at the resort front desk. Your checked bags should arrive on the inside of your resort room within 3 hours of the time you check-in at the resort ... they'll get to the inside of your room whether you're in there or not, so need to sit around and wait for them
At some point after the bags are off-loaded from the airplane, workers start separating out the ones with the bright yellow DME luggage tags. These tags are sticky yellow paper, with all sorts of pre-printed information (name, reservation number, resort name, etc) AND a barcode. This barcode is scanned 5 separate times on the route from airplane to resort room. The bags are brought to Disney's luggage sorting facility on the grounds of the airport. There, they are separated by geographic zone and then by resort. They are loaded into cages and the cages are loaded into DME luggage delivery trucks. The cages are delivered to the resorts, and then the resorts' Bell Services cast members take things from there. The barcodes are scanned 5 times and the delivery trucks are tracked by GPS, all of which means that Disney knows where your bags are at all times.
That's how DME works on your arrival day.