reward will appear by itself once all of the skull fossils are found.
In the underground.
saltwater
First, go underground using the Explorer's Kit. You get the Explorer's Kit in the Digger Man's house in Eterna City. His house is right next to the Pokemon center. Use your Explorer's Kit OUTSIDE OF THE HOUSE and you'll go underground. Here's a vital part of Skull Fossils and Armor Fossils. If you don't have the National Pokedex, and if your trainer ID is an odd number, you can find Skull Fossils underground (though uncommon). If your trainer ID is even, you'll find Armor Fossils. Once you get the National Pokedex though, they reverse. Odd is Armor Fossils, and even is Skull Fossils. Skull Fossils- Cranidos Armor Fossils-Shieldon
I'm not sure what fossils you're looking for, but you can get Helix ,Dome,Amber,Armour and Skull Fossils. In Diamond, you can get a Skull Fossil. In Pearl you can get a Armour Fossil. All other fossils can be gotten after both games.
Armour,Skull,Helix,Dome,Old Amber and Root Fossils.
Infinity
The Skull and Armor Fossils will be given to you by a player in Twist Mountain, he will give you a fossil on a daily basis except for the Plume and Cover Fossils.
shotgun
skull fossil and amour fossil
Of course. You can get them in Diamond, Pearl, Platinum. Go underground using Explorers Kit found in Eterna City (digger man gives you it his house is next to Pokemon Center) then, if your trainer's ID is even, you find ONLY armor fossils. If it's odd, you find ONLY Skull Fossils. once you get the National Pokedex, though, they are reversed. Odd, Armor fossils, Even, Skull Fossils.
skull fossil: Cranidos Armour: Sheildon
You go underground and just search. Skull fossils appear at random, but they aren't all that rare. You just have to search. Also, Cranidos Skull fossils can only be found in Pokemon diamond, and Sheildon Armor Fossils can only be found in Pokemon pearl.