From Starbound Wiki
To play Starbound in multiplayer, you need to do a couple of simple things: First, find an IP address of a server. Second, join said server. Here's what you can do to get started!
- Get Starbound Server Up & Running: Obviously you'll need to get the game up and running. You can find the starbound_server.exe in your Starbound install directory. If you're having problems, you can right click the game in Steam, go into to properties, and then "browse local files" to find your install directory. Most likely, you're going to find it inside the "win32" directory. Once you have the game loaded, click "Multiplayer" in the main menu.
- Hosting and Joining: To host a game, launch the server application and make sure port 21025 TCP is forwarded to your local IP. When trying to give your IP to your friends, don't give them your local IP, instead use the IP from WWW.whatsmyIP.org. To join a game, launch the game application, go to multiplayer, and type in the server address. (For people connecting to their local server, you may use 127.0.0.1)
- Playing Together & Partying Up: When your friend spawns he will be in his/her ship, simply click on the plus sign under your avatar in the top left of your screen, type in your friend's name and invite him/her to your party. Your friend can now click on your avatar in the group window and instantly teleport to your ship! Although, it gets annoying every time you die, you beam up to their ship.
- Additional Worlds & Servers: If you're a true explorer and want to branch out, why not take time for additional multiplayer worlds, with dedicated servers for lots of people. Here's a handy server list you'll probably want to check out: http://starbound-servers.net/
- If you're still having issues connecting to multiplayer, there's quite a few handy guides which will give you additional support. See here: reddit:MultiplayerGuide.
Also: check Reddit or the official forums for latest issue patches.