Originally posted by radaghast
Ok being a n00b myself I must warn other n00bsters about certain things in Civ3 that you absolutely HAVE to know or there is a good possibility that you will stay in noob hell forever! (Im serious it is possible)
First thing is a little something that gets batted and kicked and smacked around here a bit but no one has really just come out and said it. If they did, they would have saved this n00b COUNTLESS hours of N00b hardship. 
#1 FOR THE LOVE OF GOD DO NOT FOR WHATEVER REASON PLAY CHEIFTAN!!!!!
Bottom line. It's twice as hard to play as the next level. Easily. TWICE AS HARD IF NOT FOUR TIMES AS HARD!!
I tried getting into this game years ago. Tried on Chieftan probably 8 or ten times and was unable to get anywhere in any game. Gave up until recently. Why should I try the next level when I CANT BEAT the first? With Civ3 that whole way of thinking is out the window. The game revolves around getting techs. THE BEST way to get techs is to trade with other civs. In CHieftaN the civs are ubor dumb and evolve super slow. They also don't get out and about with their boats quickly which is bad because you can't trade with those you can't see. Because you have to research EVERY tech yourself you'll be lucky to get out musket men before the year 2050 in Chieftan. (if your n00b)
I kid you not. Chieftan is not "easy" it is "stupid" it is "hard" it is "slow" GO WARLORD RIGHT AWAY!
#2 Stack peasants! Two is good. Three is better! Make sure your city has roads, food, and mines. Leave NO patch of earth bare and remember that improvements can be built on even luxuries. Don't build a road and move on. Build a road, then a mine, then move on. That saves you tonnes of moves.
#3 Small cities are NOT useless! Plant forests next to those crappy towns. (when you get construction)Two forest squares with two peasant wood choppers on each. I actually go nuts with the wood chopping, stacks of four peasents on three squares. You can reforest early on but not right away. I can't stress how much this helps small towns grow. That "87 turns left" means nothing when you have a good forestry system. I built a harbour in a #2 city in a few turns!
#4 Defensive units for DEFENCE Offensive units for offence. Try it the other way around and you'll lose, lose, lose! (IE pikeman attacking=BAD swordsman defending=BAD! It doesn't matter how many units you have stacked. I've seen a single defending Pikeman take out a stack of 7 attacking Pikeman. 
#5 (IMO) Don't worry to much about wonders (unless culture victory is on) The 32 turns it takes to build Galileos Supreme Project of Ubor-Cheese "could" be better used pumping out a military.
*edit-there are a few wonders that are worth building such as pyramids/great Library/Theory of evolution (two instant techs I love this one)
#6 (IMO) Don't study techs. Keep the sliders at zero unless your ahead. Make money, buy them from others, wheel and deal. Keep up to date on who has what tech. Buy one then use it to get another off somone else. It seems to me that it is faster this way but I'm still a noob so I'll get flak for that I'm sure 
*edit- I have started studying a few techs later in the game when the other civs have nothing to offer to stay ahead of the curve.
#7 Build cities close together. Any spaces in your culture borders invites settlers to build and block your passage through your land. Remember the culture border (outer border) does not reflect the squares that your town can work. The inner white border does.
#8 Distribute your city people manually. Sometimes they will work a crap square when there's a gold deposit right next to them. Keep an eye out for that. And never automate workers. Automating is for kids 
#9 Try to mainly build units that can upgrade. Swordsmen are great early but just try to build a pike for every sword. Comes in handy as hell later on.
#10 Make sure your aware of the victory conditions. I've read stories on this forum where somone will be one step away from a sure win, only to be beaten by a victory condition they didn't know was activated.
#11 Read the threads on this awsome forum.
#12 Ask the Civ how much it wants for a tech before offering $$$ Sometimes you will be suprised. IE he will ask 300+world map for a 1000$ tech!
#13 Don't "do" wealth. Get that no.2 town that has no forest to build a musket man in 98 turns. That way when you come back to the town you can spend the sheilds on whatever you want. Getting them to build things that take time is the only way to save up those shields. When you see a tonne of shields in that town later on, switch production to something that you can use, IE a bank or whatever.
Sorry, radaghast,
but I have to disagree to almost everything you wrote (at least to much of your major points). Please let me explain:
#1. Chieftain may be fine for anyone being new to the concept of Civilisation, but for sure it is not a challenge too hard.
#2. Three workers is not automatically better than having two of them. Check with the first worker (assumed that you switched on the extended command knobs) how long it will take to perform a certain task at the given tile. Re-check then with the second and the third (by moving the mouse pointer over the appropriate button). Often, you will find that worker1 will use 4 turns, worker2 will use 2 turns (as it adds up with no.1) but worker3 might use 2 turns as well (due to rounding errors). So, in that case you may move him one tile further and start building a road, or whatever.
Don't mine the new roaded tile in any case! Often, it makes more sense to improve your trading net first (as roads will give you commerce = money). That money may be spent for research or just put to your treasury for later times. Furthermore, roads may allow your units to move quickly from the one edge of your empire to the other. Often, this decides about whether you or the AI might get a certain spot (think of the settlers, which have to move over there)
#3. Although it boosts you enormously when you can chop forests, since ages (in matters of game patches) the "chopping factory" doesn't work anymore. For sure, it doesn't work at C3C, but doesn't at PTW 1.27, either.
But, of course it is right to chop a forest which is already available. Chopping costs 4 turns (hmm, maybe you have to be industrious for that - otherwise it would be 6 turns) and gives you 10 shields, while mining takes 6 turns and then additional 10 turns to get the same amount of shields as the chopped forest.
The 10 shields you've got from chopping may be put into the construction of a granary or a temple (remember, at Warlord level you will only have 3 content citizens at your city)
#4. Correct, but have a look to what the other ones have explained in this thread about making use of units.
#5. Wonders may be important! But not every wonder will be important in your situation! Naval wonders may be good on archipelago or island maps, but don't have to support you very much on Pangea maps. But, they add to your culture, and will give you some benefits, anyway.
So, analyze your situation. Where am I, what plans do I have for the future, and does that wonder fit to my plans? If yes, do everything to get it. If no, let somebody else spent the shields for it.
Especially, I would like to put everyones attention to the Mausoleum of Mausollos (seems to be the most underestimated wonder of C3C)! A great wonder, if you can construct it in your capital or in another highly productive town with access to fresh water! It makes additional three citizens content in that city, so that it should be able to grow to size 10 easily (think of the fresh water!) without the need to have to have a cathedral in there.
#6. Completely wrong! (Sorry, no offense meant, just my personal view...)
Try to get your own techs. Those you will have for sure, about what you might get from your neighbours, you only can guess. Your money doesn't help you anything while being in Despotism and being at war with the two civs you currently know about (Note: this depends very much on map size and number of opponents).
Sell your techs, but have a look at their benefits, first! If you just started to construct the Great Library (e.g.), it may be advisable not to sell Literature to an opponent with productive cities. The whole thing could end up with him/her finishing it 2 turns in advance of you.
If you've got the GL, you might give the buying/selling of techs another thought.
#7. Build cities, where it makes sense to do it and in a way which fits to your favorite playing style (although I admit that you might be uncertain about your playing style, when being new to the game). Since without fresh water (rivers and lakes) or aqueducts your cities in the beginning are limited to size 6, for the very first cities an overlap of their productive areas may be acceptable, this may limit them when being somewhere in the middle of the Medieval Era.
But make sure, that you don't put your cities to far away from each other! Think about the travel time from one city to the other (for instance, from your military center to the cities near the current border, or where your settlers are produced). Keep in mind, if their productive areas are not adjacent, you will loose tiles to use later on. Or, you put a new town in, but then you have the effect of overlapping productive areas.
#8. To this, I agree. Sometimes it is annoying to have to move your workers by hand, but I never automate them, either.
#9. Agreed.
#10. Agreed.
#11. Not agreed!

(Just kidding! - Of course, do it!

)
#12. Agreed.
#13. Not agreed. The decision about if and when a city should produce wealth depends on the situation of your empire.
Ok, that's it for the moment. Again, no personal offense was meant by me commenting your suggestions.
Almost everything is impacted very much by the map size, the map style, the number and attitude of your opponents.
So, there almost is no "Do exactly this and you will benefit from it under all circumstances".