Hey Other,
Welcome to the Cookshack Nation. You're gonna love your Smokette.
You're probably going to get a lot of different answers, but here's what I do: Soak the shelves in hot soapy water for 15 minutes or so. (I bought a shallow plastic storage bin to use for this) Meanwhile, assuming you lined the bottom and covered the top of the woodbox with aluminum foil, dispose of the foil and wipe the bottom grease free with paper towel. Back to the soaking racks, scrub the gunk off with the scrubber side of a kitchen sponge. Put in dishwasher along with the side shelf holders.
Total time: 30 to 40 minutes.
After you've used your Smokette a bit more, you may notice some "stuff" sticking to the sides. Scrape this off with a putty knife when necessary.
May be interesting to read what others do.