Inside the Relic Castle, there is a Backpacker. Talk to them, and the offer you either the Cover Fossil (Tirtouga) or the Plume Fossil (Archen).
After you complete the main story, a worker on the Mistralton side of Twist Mountain will give you 1 random fossil daily from all the previous games (Red/Blue through Diamond/Pearl).
To restore a fossil to life, go to the Narcene Musem and talk to the woman behind the counter on the right side with an empty space in your party (if you are full, she will hold onto your pokemon until you make room).