After Final Fantasy XIII-2 is released, Square Enix plans to keep the game fresh with plenty of DLC content spread out across monthly releases. However, being able to actually use your new DLC items will require some in-game hunting.
If you download a new weapon, you must hunt down and defeat the correct enemy in order to get ahold of your loot. For new enemies, it's just the simple matter of travelling to the correct location to battle them. Cosmetic items like costumes won't need to be sought after and will show up during cutscenes along with other DLC items.
Regarding monster capture, you'll be able to set up to three of your own creatures (each with a specific role) to help tame beasts. If that wasn't convenient enough, your beasts will automatically switch in and out according to your current Paradigm. Be sure to keep your creature roster in order to fight efficiently.
PS3 and 360 owners can pick up Final Fantasy XIII-2 on January 31, 2012.