Originally posted by ling.speed:

What you want is a dedicated server. (check guides section or youtube)

Don't go to stupid YT for technical documentations. All you get there are demonstrations of technical processes - no way too look some detail up later, trigger your visual memory by one of a few memorable pictures of parts of a process (just one continous stream) and so on...
-> https://valheim.fandom.com/wiki/Valheim_Dedicated_Server

Originally posted by ling.speed:

Run it on your PC, or the friends PC, or buy one for pretty cheap from hundreds of server providers.

I've even seen manuals for using free cloud computing test accounts from Oracle (even free after the test period?).
The RaspberryPI may work too but they've been unobtainium for some time now. I'd recommend Thin[hackaday.com]Clients[www.parkytowers.me.uk] an old laptop or sth. like Intel NUCs

Originally posted by ling.speed:

For first two options you'd need an external IP address with ports open, not every internet provider offers this nowadays, some can be convinced to allow it if you talk to them thou.

I'd like to agree and personally do prefer opening the proper ports (firewall) with forwarding (router) but VH does use "crossplay[playfab.com]" which uses the ugly hack of UDP hole punching[en.wikipedia.org] to circumvent most firewall/router/ISP hurdles.

Originally posted by ling.speed:

If you cant assure any of the PCs running when the other person wants to play, and dont want to spend more money, then technically you could synchronize the save files over the internet, but that question is more for the google.

Haven't tried that but I think it should work kinda like this:

1. A: Set the world to local storage in VH.
   
2. A: Add the local world storage folder to e.g. GoogleDrive.
   
3. A: Share it in GoogleDrive with your friend.
   
4. B: (Create a World with the same name and 1.)
   
5. B: Configure GD to sync that shared folder with the other local storage folder. (If that isn't possible maybe junctions[schinagl.priv.at] can help.)
   
6. Always make sure the files are successfully synced.