Nice FAQ Fox Doucette, but i had a few minor quibbles:
In section 3B you say "After getting your defenders and workers you should build (in order) a Temple, a Library, a University, a Cathedral, and a Colosseum." It might be clearer to beginners if you update it to say (as i assume you do this) to alternate these buildings with producing settlers early on. Especially if they have reached size 6 and you havn't developed construction yet to build aquaducts (unless you are on a river of course).
In 3C "The resistors calm down sooner or later, and if you want them to calm down sooner, let your soldiers rest, rearm, and recuperate in the newly captured city pacifying it as they go" is nit necessarily a good idea. The number of resistors pacified in a turn is equal to the number of troops stationed, but the chance of the city reverting back to its original culture seems to be related to the number of resistors left (or maybe it is just about the relative strengths of the two cultures, and is constant as long as there are resistors left). Whatever, the point is that statining a lot of troops in the captured city doesn't stop it going back to the original civilisation, and causing you to lose your troops. Therefore it is better to spread the risk and leave the bulk of you forces in more stable cities near the border. As a rule of thumb, I tend to put only two defensive units permanently in the new city until it is calm.
For 4A it might be helpful to mention not to bother irrigating until you have Republic/Monarchy.
4B: Interesting idea about reforesting, but i tend to get a better balance mining grassland for two food and one shield (improved to 3 food and two shield with railroad) for a greater food income. Also, since this is what the automated formers, oh OK, workers, do, it saves you time. It seems counterintuitive to mine grassland, but with the removal of "farmland" from Civ2, and a slight change in the effect of irrigation, it is not a waste of a terrain square to do so.
Your advice to trade your luxury resources is fine, but it might pay to check what benefits you will give the enemy civ. For example if they already have two luxury resources, then giving them a third will give them two happy faces in cities with a marketplace, and if you only have one luxury, the added luxury will only give you one more smiley! This gives the enemy the advantage.
7A: You advise that beginners start on Pangea, but I would qualify that they should only do this on a huge map, or they will find themselves running out of room very quickly what with the enemy expanding so quickly now. It is easy to play with continents on Large and hopefully you will get an island to yourself for a little peace. if you play on Continents, (which I find makes the game a little more interesting) you reduce the wars and find it easier to defend yourself. It can eliminate (nearly) the the threat of losing workers, and bombardmen of terrain improvements by bombers.
7B: In a related point, you recommend 60% for water coverage to get more land, and therefore less war. But if you play on Continents, increasing the water to 70% gives you a greater chance of being on a big island to yourself.
7C: You suggest older world. I prefer middle-aged, because you get particular regions where you find mountains and desert etc. so it makes the tactical side of trying to expand ino various areas where you want to own a resource easier to plan. Othrewise its just random what you get on the land you own.
8A: I completely disagree with the idea that Militarism is a good way to go. It is rubbish. If you build Sun Tzu's War Academy (now one of the best wonders) then the advantage of having cheaper barracks is negated. Walls are useless and i never build them, since a city below size 6 probably isn't really worth worrtying about losing temporarily to the enemy. Coastal fortresses are rubbish as well. Getting more elite soldiers, and therefore leaders, and therefore more wonders, is quite cool, but is not enough.
9B: Disband workers during war? A bit of a waste, surely. Just fortify them in a city for a bit. Automated wrokers will often do this on there own accord if threatened.
11C: I think this is where you really do have it very wrong. Other really important Wonders that you don't mention are Sun Tzu's War Academy, Micjhalangelo's Chapel (best wonder in the game = double's effect of cathedrals, a LOT of happiness generated, and it works everywhere not just on your continent). And where on Earth is the Hoover Dam, which magically, for no pollution cost, transforms all cities with factories into +50% more production.
And you are wrong about Leonardos' workshop, upgrading units is brilliant and cost-effective and very very affordable with this Wonder. The usefulness of instantly turning all your riflemen into infrantry for a few hundred loose change as soon as you have the tech is immense, and you suggest painstakingly building a new army every time? Come on!
Getting Shakespeare's Theatre is hardly a priority either, nor is Newton's Uni, Copernicus's Obs. Those culture points are just a consolation prize for the ineffectiveness of the wonders. Build them if you are going for the cultural victory of couse.
13B: You suggest not building the Apollo wonder until you have all the prerquisite techs to build your spacecraft. Er, why? Its a Small Wonder. No like in CivII where it helps you enemy. Why not build it as soon as possible, and the intervening tech development period, build you spaceship parts as they become availabler, not all at once. Plus it generates culture.
Phew! That's it as far as suggestions for your FAQ go. I hope i didn't sound too critical - i actually found it to be an informative and enteraining guide.
PS. Great post Paeanblack, definitely the kind of incisive and specific advice that helps people improve their game. But i took issue with a couple of things you said:
First off, what version are you playing 1.07f or 1.16f? in 1.16f you really do get a flat rate of waste and corruption during Communism this time, and so if you want a globe-straddling Empire, then switch to Communism after you get Modern Armour and can afford to reduce science rate, and start conquering. Outlying cities now can have much more shield production, so even a peaceful empire thats unnaturally huge will see border improvements to production.
Second, i agreed with Fox's advice on keeping the old Civ2 strategy of science rate as high as possible. I hadn't thought of your method of only getting tech by swapping cash for it, and it clearly makes sense on really high difficulties like Diety. But i've only ever played on Regent, and i suspect most people play on this difficulty. And Fox's strategy does work on this level, after you've pulled out of the slow bronze age, if you play a scientific civ, and don't swap techs for techs but keep them to yourself, you can get ahead of everyone massively, while you can only ever keep up using your method.