Here's how it works:
1. Obtain the Fossil: You'll find the Fossil in a cave in the Jagged Pass (north of Slateport City).
2. Go to Devon Corporation: Located in Slateport City.
3. Talk to the scientist: There's a scientist inside the building who will revive your Fossil for you.
The Fossil will revive into one of two Pokemon:
* Lileep: If you have the Old Amber fossil.
* Anorith: If you have the Old Sea Fossil.
Which Pokemon you get depends on which fossil you have. Make sure to pick up the correct fossil before going to Devon Corporation.