Play the World is the long anticipated Multiplayer expansion for
Civilization III. Thankfully, it has now been packed into a single box with the original game, which means you don't have to shell out additional money to get the expansion on top of the game.
Play the World offers four different Multiplayer modes. You can opt for internet play, games on a LAN, Hotseat mode where you play on a single computer and take turns at the keyboard or play by e-mail.
Your best bet here is to play on a LAN. For some reason, the stability on the internet games is horrible. For a game like Civilization III, there shouldn't be that much information traversing between the computers. And, when you add more players to the mix, things go straight down the crapper. So if you stick with a LAN, the only problems you should have will be crashes, and those are easy to recover from when everyone is in the same room.
Within these modes, you can choose to play either turn based or on the clock. With multiple people playing, turn based is totally out of the question, as you'll be waiting forever for your turn. Simultaneous mode basically makes everybody do everything on the same turn, and that turn is timed on a clock. As the game progresses, the turns get longer, but this doesn't really flow that well with how the game is set up. Sometimes turns will be quick, which will leave you waiting for the timer to run down, and others will require you to do a lot of stuff at once, leaving little time to do it all.
Hotseat and play by e-mail are nice additions, but aren't implemented all that well. With multiple people, Hotseat becomes a hassle, and play by e-mail has many flaws regarding what you actually get in the e-mail. At best your perception of how the entire game is progressing is blurred by the information you receive, resulting in very chaotic play.