So you want to play Aground multiplayer? Sweet!
Aground has no game servers, you have to directly connect to everyone you want to play with. Steam has an API for connecting with friends using their servers, but if you want to connect with someone not on Steam, you'll need to follow this guide to connect via IP address.
If you want to play with someone on the SAME router (for a LAN party - i.e. playing with someone in the same house):
All you need to do is find the IP address assigned to you by your router. This is usually some variant of selecting your wifi connection and clicking properties/details (an IP address is four numbers separated by periods like 192.168.0.8). This site has a good guide with pictures to find it on all the operating systems Aground runs on: https://www.howtogeek.com/236838/how-to-find-any-devices-ip-address-mac-address-and-other-network-connection-details/
Write down the IP address, and then host a save on that computer (Multiplayer -> Host Game). On all other computers, select Multiplayer -> Join and enter the IP address for the host you wrote down earlier to connect. As long as the computers are on the same network, you should have no trouble connecting. Make sure you use the HOST's IP address you wrote down, not the IP address of the computer you are using to join.
If you want to connect to someone over the internet:
Over the internet, you need to use your public IP address, not the one assigned by your router. Luckily, this is much easier to find - you can literally google search "my ip" and google will show you your public IP address.
There's one catch, unfortunately. If you're behind a router, then that router has to have port forwarding set up, or no one will be able to connect to you via public IP. If you're curious, this is because routers can have many devices connected to them, but there's only one public IP address, so it doesn't know which computer someone is trying to connect to.
Setting up port forwarding varies from router to router, so I can't give an exact guide, but this guide works for many of the more popular routers: https://www.noip.com/support/knowledgebase/general-port-forwarding-guide/ (google search your router if you don't see it in that list). For Aground, you'll need to forward port 16124 (TCP) and port 16125 (UDP) to your computer. Your internal IP address is the one assigned by your router that I explained how to obtain above. Make sure the internal and external port numbers match for the two entries (if your router asks for it). Luckily, you only have to set up port forwarding once, and then you'll be able to host as many Aground multiplayer games over the internet as you want.
Once port forwarding is set up, all you have to do is host a save and share your public IP address to everyone you want to join (keep in mind, that your IP address can help people identify you, so don't share it with complete strangers). They can enter that address to join your game, just like above.
Can I do this on my Steam version?
Certainly! When you click Join, the first option in the games list is "Join Other..." Select that, and you'll get the same connect by IP address window as in the non-steam version. You can even play with a friend using the same steam copy if you tell steam to go offline and connect via IP (obviously, I'd prefer if all players buy the game, but I won't complain if you want to play with friends in a LAN party using one copy of the game). While steam is offline, you can't connect to players via steam and achievements won't sync, but achievements will sync the next time you run the game with steam online - just make sure you don't actually go offline, just set steam to go offline.
Feel free to post a comment here if you have questions! And if this confuses you, know that this was how everyone had to connect back when I was growing up!