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. Upgrading awareness through merits or other means increases your chances of finding better items.
There are two merits associated with the dump: 'Scavenger' for finding 1,000 items and 'Eco-friendly' for dumping 5,000. It doesn't matter what items these are.
An example of finding an item is: You found the item Brick trashed by Chedburn!