Unless there is some pressing reason you want to pick up your bags yourself, you don't need to go to baggage claim. If you want DME to take care of your luggage for you, you will have to affix the yellow DME luggage tags to each checked bag. Then...say goodby to them, until they arrive at your resort. Yes, it does take a few hours (3 or so from the time of resort checkin) for the luggage to get to your room. But, you should always pack a carryon bag with any essentials for the first part of your arrival day...the airlines could misdirect your bag(s) and if you have a carryon packed, you can go about your day, without those checked bags right there.
If, for whatever reason, you want to collect your own checked bags...do not tag them with the yellow tags. (those yellow tags alert the baggage handlers that the bag is going to a WDW resort, on a special luggage truck. they are pulled out and set aside, they aren't supposed to make it out to the public baggage claim). So...you will go to the appropriate baggage claim area for your airline...Side A baggage claim if arriving on Side A, or baggage claim for Side B if arriving over there.
Then, you will need to go to Side B, level 1 to get to DME. If you are already on Side B, baggage claim (level 2), you just need to go down a level. If on Side A, you will need to go to level 2 to get your bags, then up to level 3 (the level you arrived on), cross over to Side B, and go down to level 1 for DME.
Hope that helps rather than confuses you!