Bones are obtained by killing many monsters. Virtually all humanoid NPC's will drop bones when killed. Many monsters including goblins, animals and trolls will also drop bones.
There are many different kind of bones. While Humanoid and smaller creatures drop regular bones, other monsters like Green Dragons and Werewolves drop their own kind of Bones. These bones are Dragon Bones, Wolf Bones, Burnt Bones, Big Bones, Baby Dragon Bones, Monkey Bones, Jogre Bones, Zogre Bones, Ourg Bones, Fayrg Bones, and Ancient Bones as rewarded by Father Aereck after the completion of the Restless Ghost quest.