Yeah you do it yourself. The transfer case is easy to drain...on the backside there's a "harmonic balancer" with 4 bolts. Remove this, and there will be two plugs that require a 3/8'' drive socket/extension to remove. Drain at the bottom and fill the top plug until it runs out. It takes Mercon ATF. I prefer at least synthetic blend, but this is not the place to argue about that.
I haven't done my Explorer yet, but for the tranny you'd have to pull the pan. This, however, would only get out around half of the fluid, the rest being in the torque converter and stuff. What I've done with other vehicles is to do the pan, then replace the old fluid with new fluid, and with the return line from the tranny cooler off, start the truck and run for a moment to pump fluid into a container. After maybe a quart, stop, add another quart, repeat...until it runs out clean.
Don't do that though until someone more knowledgable replies and says it's okay to do with an A4LD. Um, you have an automatic, right? If it's a manual, then it's a lot simpler, and pretty much like the X-fer case but with the plugs on the driver's side. Again, Mercon ATF.
The rear axle cover can be removed, draining the fluid. Either use a new gasket or ATF, whatever satisfies you. This uses gear oil, 75w140 if you can find it, but I've used 80w90 just fine and has been said on the board to be okay.
I believe the front differential needs to be pumped out through the check plug.
There's your power steering fluid too. Maybe even coolant if it was salt water?