You can use DME no matter
which airline you fly!
For
arrivals, all travelers get the exact same services:
Reserve DME in advance
Attach one yellow luggage tag (which you will receive with your DME packet) to each piece of luggage you will be checking at your home airport
Go to airport. Check in for flight. Hand over luggage you are checking. Wave goodbye - you will not see these bags again until some time after you get to your Disney Resort room

Go through Security. Board plane. Let Captain fly you to Orlando.
Get off plane. Take tram to main airport. Follow waving Mickey hands (while they exist) or signage to Terminal A, level 1.
Get in DME line. Check in. Go to line for your resort's bus. Board bus. Let driver drive you to your resort.
Get off bus. Enter resort. Check in. Go to (most likely ready) room. Drop off carry-on luggage. Go off and do something - swim, visit a park, have a meal...
Go back to your room. Wave hello to your checked luggage. Enjoy the rest of your vacation.
For your
return trip:
ALL Disney resort Guests may use DME - a packet with your specific information will be on/under your door the day before departure.
If you are flying United, Ted, Delta, Song, American, JetBlue or Continental (participating airlines):
Check in at Airline checkin counter at resort. Give them your luggage (or have Bell Services bring it down) Wave goodbye to checked luggage, you won't see it again until you get to the luggage carousel at your home airport.
Show ID. Get boarding passes.
Be at DME pickup three hours before departure or as directed in your DME packet.
Board bus. Let driver drive you to MCO. Get off bus. Go through Security. Board plane. Let Captain fly you home. Get off plane. Go get your luggage. Go home. Start planning next trip.
If you are flying any other airline, you can still use DME! You simply bring your luggage directly to the bus, where the driver will load it underneath the bus and unload it when you get to the airport. Go to your airline's checkin counter, self-check kiosk (yes, you can do this even when checking luggage) or Skycap area. Check in. Go through Security, yadda yadda yadda.