The first two chapters of the manual explain only how to install the game and how to use the mouse/keyboard interface to play. The first thing it mentions that is worth commenting on is how to set up a game. This is in fact a very important decision, as it will greatly affect the nature of the game being played. I'll go through each part of the setup screen in detail here, with info on each part.
World Size: OK, how long of a game do you want here? Obviously, the larger the map is, the longer it's going to take to play. What you might not realize is that larger maps are going to take your COMPUTER longer to play as well. Huge maps cause slow computers a ton of problems; if your computer has close to the minimum requirements to run Civ3, it can take as much as 5 minutes (or longer) waiting between turns for the AI civs to move all of their units. This is the reason why I stay away from huge maps. Many players like the big ones though, so go ahead and play them (but don't say I didn't warn you...)
Map size also affects other things. The cost to research tech increases with each map size (because you will have more cities), as well as the optimum city number (a number that partly determines how much corruption your cities will have). On tiny maps this number is 12 (meaning once you get more than this number of cities, you will start seeing very high corruption levels away from your palace), small is 14, standard is 16, large is 24, and huge is 32. The smaller the map, the fewer the units involved in combat and the more important each battle is, with the reverse true for larger maps. Also keep in mind that there will be more goody huts on larger sized maps, increasing the value of the Expansionist civ trait. I personally like Small and Standard maps the best, but that's a matter of opinion.
Land Mass and Water Coverage: Here's the other biggie in determining how your game will be played out. More land means more cities, more units, more trading; more of everything. Fewer land tends to lead to more conflict as well. Again, the more land you have, the slower the game is going to go as you manage more of everything. The three land masses all play very differently. Pangea maps seem to be a favorite of many players, since they can completely ignore ships and just focus on running over every other civ. One thing to keep in mind on a Pangea map is that if you get into a war with another civ, they WILL come after you eventually. The AI is hopelessly bad at seaborne invasions, so Pangea maps may give them some slight advantage. Keep in mind though that not every Pangea map is actually a single continent, for reasons I don't understand. Continent maps are a compromise between the other two; usually there are 2 or 3 main continents that the civs start out on. The goal is usually to secure your own continent, and then proceed from there. You will have to deal with ships if you plan to invade another continent though. Continent maps are also very popular. Archipelago maps are the type least played, probably because they are the hardest to achieve a conquest/domination victory on. It is very hard to kill another civ, since they will almost always have another city on an island out there somewhere. Loading and unloading units from ships can be a major pain as well. Because of this, it's possible to fight wars on archipelago maps where you never see any forces of the other civ; these are often called "phony wars." Archipelago maps can be a lot of fun to play on though, since they are the only area where you can expect to see any kind of naval action. I've played all types of maps, and enjoyed different things about each of them.
Climate, Age, Temperature: I don't really think too much about these options. Normally I just set them all to random when starting a game. Climate determines how much total food there is in the game; an Arid game will have more plains/deserts and a Wet game more jungle and rivers. Obviously there is greater food potential in jungles, but you will have to work harder to get it by cutting down the jungles (which takes forever). It's your call on what you like better. The Age just determines how clustered the terrain types are; pick 3 billion if you like large stretched of the same stuff and 5 billion for diversified terrain. Temperature determines whether you will have more tundra (Cool) or desert (Hot). Neither type of ground is very good, but keep in mind you can improve the food output of desert through irrigation while you can't do much with tundra. I generally like to set this section of the setup screen to random though, and play with whatever comes out. You'll have to see what works best for you.
Barbarian Activity: Well this can dramatically affect your games! (see Epic4 if you don't believe me) I don't really like barbarians very much, but their presence and how extensive they will be can really change the nature of a game. Turning them off is one way to deal with them, but keep in mind that there will be no goody huts either if you do this. Sacking barbarian camps can be a very significant source of income in the early game as well, so remember that you are cutting off a possible source of income (and promotions for units) if you turn off the barbarians. Roaming barbarians will have them occur at an easily manageable level. Restless will be a bit more tricky, and Raging Hordes will force you to divert a significantly higher amount of early production to defense to deal with the barbs. I've played on all of them, and the unprepared can really get nailed on the highest setting if they are unfamiliar with it. Choose your level of barb activity with care.