A few words on very basic strategy:
(1) Build roads. Roads are good. Roads are very very good.
A related rule:
(2) Build next to rivers.
These are the only two ways to consistently get commerce early in the game (other than certain bonus resources). Yeah, ocean squares give you commerce, too, but they don't produce enough food (until you have a harbor) to do you much good, and even then they aren't producing shields for you.
(3) Build mines on grassland under despotism. This is new to civ 3, but it's the best way to get your shield production up in the early game, and irrigation is useless to you until you switch government (which you should do ASAP)(to Monarchy if at war/wanting to be at war, possibly the Republic if at peace/wanting to be at peace). Once you switch, you'll likely want to replace some of those mines with irrigation so your cities can grow.
(4) Don't let the city manager make all the decisions on where your workers work. The city manager's priorities are very much focussed on food, but you don't need to be producing any extra food when you have a size 6 city with no aquaduct, or during the long stretch that you'll have lots of size 12 cities with no hospitals, so you may as well work on maximizing shield and commerce output.
(5) Plan ahead. This applies to every aspect of the game, but here are some examples: decide which techs you want to develop ahead of time (definitely don't just take the ones they suggest). I find in civ 3 that it's good to develop techs that reveal strategic resources ASAP; after bronze working and cermonial burial (got to have those spearmen and temples), I tend to go straight for the wheel and iron working, so I know where the horses and iron deposits are.
This also applies to wonders. In the ancient world, only one wonder-- the pyramids-- lasts the whole game, and it has a great benefit, so make sure you build it. The great library is nice, too, if you are in contact with lots of other civs, or if you don't want other civs to get the benefit. All the other ones are worthwhile-- for culture if nothing else-- but pyramids truly rock.
(6) Get and maintain tech advantage. There are other strategies that can work (I've seen some interesting advanced strategies for just building up money, no tech), but the tried and true method for civ is to put every bit of your resources you can into tech. The equation is really simple: if you have tech advantage, you win. If they have tech advantage, they can walk all over you.
How do you get tech advantage? It all starts back at (1) and (2).
(7) While you're learning to play, be very selective about starting position. It can be fun for experienced players to take whatever map and whatever starting position they're dealt, but as a newbie, I'd recommend quick starting until you get a nice, sweet setup (like, say, settlers start next to a river with cows and/or wheat and grassland with resources in sight).
There are a few basics off the top of my head; dunno if it's what you're looking for, but your question was pretty broad....
