We love ME, particularly my DH - it's that point when he begins to relax into his WDW state of mind.
You provide your airline info in order that they can be up to date on your expected arrival time (in case of delays). You receive yellow baggage tags (2 each) with each persons name and your resort printed on them. If you want ME to collect and deliver your luggage use these tags on each bag. If you prefer to pick up your own luggage do not use the tags.
When you arrive proceed to the ME counter and checkin. (I believe the lower level of the airport

, but I'll let someone else be more specific, I'd hate to get you lost.)
If you're collecting your own luggage, do that before going to the ME checkin and bring your luggage with you. The bus driver can load it for you when you board.
After check in you will enter the first of many WDW lineups

but don't worry, it shouldn't be long, we've taken 3 times and never waited more than 10 minutes. Pull up a piece of carpet and introduce yourselves to other happy people on their way to see
Each bus normally stops at 2 or 3 resorts. Settle back, enjoy the video and the scenary, your almost there.
Your luggage will be delivered usually 3-4 hours after your arrival. Don't wait for it, check in at the resort and go play. It should be in your room when you get back.
Going home is similar in reverse, if you're flying in the US your can do your airline check of your luggage at the resort. We're from Canada so we can't use that service.
Unfortunantly, they expect you to board the bus 3 hours prior to your airline departure which some people really do not like. It does cut into Disney time, but we've found it takes the "hectic" out of the return to the airport, and normally allows us to grab a bite in the airport which our connections never seems to allow time for. (although getting to the bus on time can be a little hectic...

)
Hope that helps.