In Sinnoh, when players travel underground, they can find most of the fossils by digging, along with several other rare items, potentially. After getting the National Pokédex, they can also find the five fossils from the previous three generations.
In Johto's Generation IV games, fossils can be found randomly by smashing rocks. The Dome Fossil is exclusive to HeartGold, and the Helix Fossil is exclusive to SoulSilver. The Old Amber can be found in both games.
In this generation, fossils are considered to be normal items, and can be held by a Pokémon and traded to another game.