Basically, you tell the Finder that whenever files show up in Folder A, it should run a script to process them (e.g. to move all of them to Folder B):
1. Use Automator to create a Folder Action with a "Move Finder Items" phase that puts items in the target folder that you want. Actions of this type also have a source folder setting.
2. Save the workflow as a Folder Action.
3. In the Finder, you can then right-click your source folder (including the Desktop, if you start from your Home folder) and under Services choose "Folder Actions Setup". The Folder Action that you saved from Automator will now be available in the list.
Now, whenever anything shows up in the source folder, the script will run to see what to do.