Susan,
Trading actually occurs through the swap tool. You add the items that you are interested in trading.
As you review the list of what others have available, you will notice a row of 5 stars next to each item. These stars represent your 'wish list'. You can click on 0 through 5 stars to indicate how bad you want an item. As people 'wish list' things, you will see how many are hoping to get that item beside the stars. It's kind of a way to check your competition and also lets the person with the item know that they may want to make more available, if possible.
When trading starts, each item offered will have a new button appear beside it that allows you to 'call dibs'. To call dibs, you need tickets, which are allocated by the system automatically. On the first day of the swap, at about 8:00pm, everyone will get 1 ticket. On the second day, yuo'll get 2 more, 3rd day: 3 more, 4th day: 4more, etc. Tickets are rationed at the start to give everyone a chance. As we approach the end of trading, I will most likely change the system to give some ridiculous number of tickets each day.
Now, here's the interesting part... you actually earn back your tickets when people start to call dibs on your items. So, if you make a dozen of something that people are really looking for, you'll get some percentage of each dib credited back to your ticket count. The number of tickets that you end up having available gets interesting!