You could use something like GameSpy; however, almost all of the servers / players you encounter will probably be international, which you probably don't want. What you need to do is look around at the various local gaming "services". Here's a few to get started, I'll add any others that anyone mentions to the list:
Have a look at what games they run servers for, pick one that you want to play, and connect to it The exact procedure for connection to a server varies from game to game, of course.
As far as Steam goes, it's an online content distribution system run by Valve; I'll let someone else explain it in more detail, since I don't play Valve games, but basically you use it to download updates and stuff for Half-Life / Counter-Strike / etc.