You need to set up a port forwarding first on your router then you can proceed to next step where you can download the Valheim Dedicated Server from your Steam library it's not in the game list but it's listed as tools app, you can type valheim in your Steam library search bar and it should be appear on the list below.
But it still require you to run and let the file open to make it online, not the game but the server file it should be appears like CMD window (command prompt), if you really want to make it online all the time without you having to turn on your computer you have to pay for the dedicated server hosting.