Local files can be found at:
Windows: C:\Users\USERNAME\AppData\LocalLow\IronGate\Valheim
Linux: .config/unity3d/IronGate/Valheim

Steam Cloud save folder:
Windows: Steam\userdata\NUMERICSTEAMID\892970\remote
Linux: .steam/steam/userdata/NUMERICSTEAMID/892970/remote

There's some more info on the pinned FAQ thread. It should be a simple matter of sending the files over and copying them to the correct location.