Ill assume you have the GameSpy software since you mentioned it. If you dont have an account, use the Login Wizard to create one. GameSpy Arcade (GSA) is still free, as long as you want to put up with the adds. Once you login you should see an icon on the left for any GSA supported game on your computer. If there are no Icons, in the top left click GAMESPY, then SCAN FOR GAMES. If that doesnt get it youll have to do it manually from GAMESPY / OPTIONS / GAMES / MY GAMES. Once you have the icon just click it then PLAY MULTIPLAYER (after you close the addvertisment). Now you are in the lobby for the game. The top section shows the rooms where games are organized. The bottom shows the Lobby chat and the names of all the players in that game's GSA area, on the right. To join a game click on a room with a yellow square and no key, to the left of its name, then click JOIN GAME. Once in a room there is a new chat window for only those in that room. From here you will click READY at the top of the chat window. At some point, once terms are agreed on, the host will launch the game. SFC2 will start, just wait until you see the Screen that has a JOIN button at the bottom. Click JOIN when you see a game appear above. Choose your ship then supply it. When every one is ready the host will start the game, you will die shortly there after.
You must have the game patched up to 2036. Do not go into a GZ titled room until you have a GZ account (you'll learn about this later). The icon for SFC2 only says "Empires at War". None of the SFC games works very well with firewalls or routers, so you might want to disable them or create a DMZ. You will be asked to join a fleet a some point, ask what race they are, and dont be afraid to say no thank you, new players are in short supply, you will be asked by another fleet. Here is a few of the older fleets KOL, USMC, RDA, FEDX, KWG, RDA, RIP. They will train you on the tactics of the game, the older fleets are probably better about their training than newer ones.
I hope this helps some.