When i downloaded my DLC (Xbox 360) For example, Operation Anchorage, i got a distress signal. When you get it a little window pops up on your screen and it says something like "A distress signal from the outcasts has been sent across the wastes. It seems this message is only meant to be heard by certain people (People that have dled it!)" Then you make the thing your active quest. Also youll get a new quest when you get the signal.
Or if you want to know how to DL DLC you go to Marketplace (Xbox 360). You need xbox live (Obviously)