Ok, I figured it out myself. I'll post for the benefit of others, though. If you have an account, log in to the Global Link site. On the lower right of the page there should be a rectangular orange button. Choose that. Then choose the skin you want from the list. If you can't read Japanese, select them one by one until you find the one with the picture of what you want (I think they all have pictures). Click the button to confirm you want it. I think then you're taken to a C-Gear-themed page and it gives instructions for what to do after you confirm you want that download. Turn on your Black or White game, and go to the Wi-Fi on your C-Gear. Choose the Game Sync option (the big option on the screen). Connect and pick a Pokemon to put to sleep temporarily. After this, the game will close the Game Synce connection. Now, on the Global Link site, on the main menu with the circle of rotating click-able options, choose the red one to customize. You'll see your list of options by picture on a scale. Choose the one for each section you want to use. Confirm the changes by clicking below. Then go to your Game Sync on your game again and wake up your Pokemon. It will tell you your changes have been applied, and it will disconnect from the Game Sync and take you back to your game, and presto, the changes are applied. :)
I do have one question right now: when I choose a skin for my C-Gear or Pokedex, can I keep it forever? What if, say a new one was released and I wanted to switch to that for a while, and the one I was currently using was no longer being distributed. Would I still be able to go back to it later since I had it before, or would deselecting it temporarily mean I could never go back to it since it was no longer under its distribution period?