With the full version of Minecraft multiplayer, the possibilities are endless! You can either run your own server or join one of the hundreds/thousands out there!
Running your own Minecraft server
If you are running a Windows computer, setting up your own server is very easy! Download the Minecraft_Server.exe and run it.
If you are planning on running a Minecraft server on a OS other than windows you can refer to this wiki article. You will need to download the minecraft_server.jar and run it with Java