Cori,
A notification will appear in your system messages when the swap starts. At that point, you will likely have to "refresh" your wishlist to get the change (addition of little treasure chests to the listings) to appear on your page. Then, click a chest, follow the directions, lather, rinse and repeat until you run out of tickets.
When you refresh, click the "exclude no quantity" button above it also. This will prevent accidentally trying to dib on items that are already gone, and allow you to focus on what is still available.
You'll probably mess up some at first, but each evening will get smoother.
I go through my wish list and clear out everything that I've already dibbed on, and the things that are already gone, and re-prioritize my list after the dust settles each evening.
Have Fun!