The voicechat in WoW only turns on if you are in a group, I believe.
When it does work, you will see a small audio icon next to the player that you hear a voice from. The problem is, many players do not use the built-in voicechat.
Many players use external programs, specifically Ventrilo. Even then, you will need to see if others have a chat server for Vent, ask for the IP, pass, and port number for the server, and if everyone in your group wants to use Vent.
Your best bet is to wait for someone else to offer for you to join their Vent server.
If you seriously plan to chat vocally with other players in the future, I suggest installing Ventrilo.