Copper deposits in Valheim can be found in the Black Forest biome.
Copper is abundant in the Black Forest of Valheim, a biome that shares borders with meadows. This is the second biome you're supposed to progress in in Valheim, so the gear you designed to defeat the first boss will get you started in the Black Forest. That said, it's still a deadly zone, full of gray dwarves, skeletons, and trolls. Lone trolls can push you into an early grave with a single attack if all you're wearing is basic leather armor, so you'll want to mine that copper as soon as possible to craft better gear.
The copper deposits at Valheim appear as giant boulder-sized mounds in the earth covered in green mold. You should also notice a line of copper streaks in the rock, and all you have to do is start whaling on the mound to harvest the copper. Each piece you smash the mound will net you a piece of copper on average, and you will also reap a stone bounty. Copper ore is heavy - a full pile can easily clutter you up - so if you're planning on getting rid of the whole hog, you'll want to get rid of the stone.
This shouldn't be a problem, however, since the starting pickaxe in Valheim breaks the moment you collect ten copper. Do yourself a favor and create an outpost in the Black Forest where you can unload your ore and repair your pickaxe, unless you like wasting your time darting between your first base and the Black Forest with only small dashes in your inventory. You will need the copper to create the forge, but the ore must first be smelted. Since Surtling Cores are also found in the Black Forest (which you can read more about here), it is best to set up your smelter and furnace at your Black Forest outpost to melt more efficiently your copper ore while you mine more.
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