Where do get a skull fossil in Pokemon platinum version?

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