If it's any consolation, we all started out confused at some point
But I fully agree with Kaboth - once you get the hang of it, it's a lot more fun (and more rewarding, I've found!) than Civ2, because it uses much cooler models for things like trade, diplomacy, culture, borders etc etc etc. It's a lot more than better graphics, believe you me - but, yes, that does mean that you have to figure out how it all works...
If you have the time, the succession games are a great source of knowledge (even if they do take a lot of time to plough through!), but if you have any specific questions, just post them here! I started reading these boards a few months ago, and everyone here is really friendly and helpful.
I can make a (small) start by trying to answer your questions about armies and culture... bear with me...
Armies in Civ3 are units grouped together to form a stronger unit. You can create armies in two ways - one is to build them in a city that has the Military Academy small wonder, like you would build any other unit. The second is to get a Great Leader and use him to build an army. You get Great Leaders by having an elite unit win a battle - note that this will not happen every time, but there is a certain probability of it happening (I don't remember what the exact number is, but it's something like 6% chance).
So: Let's assume that one of your elite cavalry units has just won a battle and produced a Great Leader. You know this has happened because the game will say "... has produced a Great Leader!", and will ask you to rename the victorious cavalry unit. This is purely cosmetic - you can call it anything you like. If you then right-click on the square with your Cavalry in it, you will see a new unit with attack 0 and defence 0 (and, I think, movement 3 but I'm not sure). This is your Great Leader (
not the cavalry unit you just renamed! This has confused a lot of people), and he can move like any other unit, but can't attack (not that you would want to - he's got 0 attack and 0 defence!). Note that the victorious cavalry is now "Elite*" instead of "Elite". This is to indicate that it has produced a Great Leader.
Now that you've got a Great Leader, you can do one of two things with him. One is to use him to rush-build (finish in one turn) any improvement, unit or wonder in one of your cities. Obviously, this is very powerful, and is most often used for wonders. To do this, move him into the city building the wonder (or what else you want to rush), and click on the "Hurry Production" button that will appear in the toolbar at the bottom of the screen. The Great Leader will disappear (be used up), and the wonder (or whatever) will completed the next turn.
The other use for a Great Leader is to build and army. To do this, move him into any city and click on the "Build Army" button that has appeared in the toolbar. The Great Leader will disappear and you will see a new unit in the city - called "Army", again with 0 attack and 0 defence. An army in Civ3 is a bit like a "box" into which you can put units which will then fight together. An army can hold up to three units (four if you have the Pentagon small wonder). In order to "load" units into your army, move the unit you want to load into the same city as the army, and click on the "Load" button that has appeared in your toolbar. This unit is now a permanent member of the army - it cannot be removed! You can then load more units until the army is full in the same fashion. You can then move the army as if it were any other unit, and attack with it too (that's the point of armies, isn't it?
)
Now, you're probably thinking: What's the point of armies? Isn't an army of three cavalry units as good as three single cavalry units? No, it's much better, and I'll explain why. In an army, the units share hitpoints, and to detroy the army you have to take away
all its hitpoints. So if you have an army of three elite (5 HP each) cavalries, your army has a whooping 15 HP! It will still have the same attack / defence / movement stats as the units inside (in this case, 6 / 3 / 3 ), but many more hitpoints, which means it can sustain much more damage (three times as much) as a single unit, which equates to so many more rounds of combat in which to kill the opposing unit. Try it out!
The consensus amongst Civ3 players is that armies are best used by filling them up with your strongest and fastest unit (Knights / Cavalry / Tanks / Modern Armour) and blasting away at the opposition. Another good use for an army is to fill it up with strong defenders and use it to defend key cities or locations on the map. Imagine an infantry unit with 15 HP - very close to unkillable unless you send an enormous stream of tanks at it...
That's all I can think of as an introduction to armies - but if you have any other questions, just fire away!
Now, culture. Culture in Civ3 is counted in culture points (CP) which are produced by city improvements and wonders. To see how much culture a wonder or improvement produces, check the civilopedia, or the city status screen - next to some improvements you'll see little musical note icons. These represent culture, if there are two little notes next to your temple it means that it's producing two culture points per turn.
What do culture points do? For one thing, they expand your boders. A newly-built city has zero culture. Now let's say you build a temple (2 CP per turn). On the first turn after you've built the temple, the city will have a culture of 2. On the turn after that, a culture of 4. On the turn after that, a culture of 6, and so on, increasing by 2 every turn. Note that this is cumulative - a city with a temple and a library will generate 5 CP per turn (2 for the temple and 3 for the library). As soon as a city attains a culture of 10, its borders will expand. Think of it as a village's which has been around for a bit, has become established, and its influence is spreading. Once a city reaches 100 culture, it will expand again, and again at 1000, and again at 10000. Obviously, a bigger border is good, because anything inside it is your territory, which means that only your are allowed to be in there (sending your units into the territory of another civ is violating their borders, and unless you have a right of passage agreement with them, they will ask you to leave or declare war. You can do the same if other civs trespass on your land), only you are allowed to work the land and gain benefits from resources on the land, and the map is revealed for any land inside your borders.
Culture can win you a game by something called Cultural Victory. You attain this by either having a city reach 20000 culture (on a standard map, more on larger maps) or having a total culture (sum of all your cities' culture) of 100000 (on a standard map, more on larger maps)
and having more than twice the amount of your nearest rival.
Culture also decides how your borders run when your cities are close an an opponent's. The formula is rather complicated, but as a rule of thumb, the one with more culture tends to be able to lay claim to more land. In this situation, culture also plays a part in something called culture flipping: If you and your opponent have cities close to each other, if you have a much stronger culture than him (both as a total and in the local area) then there is a chance that his city will flip to your civilisation. This is affected by many factors, including distance to the respective capitals etc etc - check out Chieftess' excellent flip calculator
http://forums.civfanatics.com/showthread.php?s=&threadid=53181 . But, in short, it's a great way of taking over opponent's cities without waging war - just build lots and lots of cultural improvements in the cities close to him and hope that one of his culturally weaker cities flips to you. However, be warned that it can also happen the other way - one of your little hamlets with nothing more than a temple could flip under the influence of his metropolis with a 1000 year old cathedral...
Lastly, any improvement that generates culture will have its culture per turn rate doubled if it's existed for 1000 years. So a temple you build in 1500 BC will start by generating 2 CP per turn, but from 500 BC it will generate 4 CP per turn. You will notice this first with your palace - at 4000 BC it will be generating 1 CP per turn, but by 3000 BC it will be making 2 CP per turn. The palace in your capital is your first culture-generating improvement - it is why your capital's borders will expand after 10 turns, because you will have accumulated 10 CP.
Phew. That was a whirlwind tour - if I've missed anything (or anything is wrong), please feel free to correct. And, if you can think of anything else you want to ask, fire away!