From this page of the Valheim game guide you will learn how and where to find obsidian deposits.
Obsidian, like silver, is a raw material that can only be obtained in the mountains. These deposits are exposed, so you won't need to use the Wishbone to help you find it. Instead, you just have to search around carefully. Large concentrations of the metal can be found in black stones scattered throughout the entire biome.
Once you stumble across a deposit, you will need to extract it. To mine Obsidian, you need to have an iron pickaxe. The other materials are too weak for this resource.