I'm just repeating what others have said, but this is my experience.
When flights and hotels have been booked with Disney UK together, they automatically reserved the
MDE for me. When I've bought the flights separately elsewhere, I rang Disney UK to add MDE reservations in both directions.
We don't get yellow tags but IIRC there is an MDE ticket of sorts included in the information package that's posted out about 2 or 3 weeks before your departure date, but you don't actualy need it to "check in", I think it basically just gives instructions. If you didn't get this, why not just give Disney UK a call to confirm that your reservations are still there, for peace of mind.
At the airport, you collect your baggage as normal (I don't bother putting it back on the shuttle to be delvered to the main terminal separately and collected at level 2 - I just take it with me on the passenger shuttle to the main terminal), make your way over to Side B of the terminal (it's always been the left side out of the shuttle station for me coming in on Virgin Atlantic) and take the lift down to Level 1.
MDE is signposted all the way IIRC. Level 1 is basically a long corridor with lots of car hire and shuttle booking desks. MDE is right at the far end. Just go to a check-in pod and give them your details, they can find you on the system and direct you to the right lane for the next bus.
Sometime on the day before your departure date they'll tie a letter to the door handle of your room - I always find it on returning at night from the last park. It tells you what time the bus will pick you up at the resort for the return journey.