The Torn City Dump is simple - Dump, and/or find.
You can add an item to the Dump by clicking the [Trash] link next to the desired item. When you dump the item, it becomes available for other players to find.
Each search uses 5 energy. With each search you have the possibility of finding an item that was trashed, or finding nothing at all.
An example of finding an item is: You found the item Brick trashed by Chedburn!