For an easy early domination victory on normal speed normal sized map on some "not to high" difficulty level with a decent map that allows for capitol to contain many cottages (9+).
-) Settle 4-6 cities and tech yourself to currency through math or alphabet (this allows you to keep researching without going broke by building wealth and also gives you +1 trade route in each city, giving you a much better way to handle the money issue)
-) Produce one GS that can build an academy in your capitol [key is to have one GOOD city with a lot of population that is increased to maximum coin generation through developed cottages and bureaucracy]
-) Settle 3-5 more cities (should end up somewhere along 8-10 cities around 1AD as a guideline with an Academy in capitol)
-) Make sure some of the core cities overlap capitol so you can help improve the cottage tiles which the capitol will take over once they gain more people.
-) Build a market in capitol [recommended buildings in capitol: granary, library, market, forge, aqueduct, and maybe a +happiness building]
-) Trade techs and fill out stuff that you really need (examples: monarchy [engineering if later going for steel, or music if military tradition])
-) Trade for happy resources and health resources to further expand capitol
-) Produce forges for better whips [for most cities, you dont need anything more than forge, granary, barrack and maybe a theatre & monument, otherwise build wealth to keep your research slider high]
-) Beeline towards Beurucracy and then liberalism until you have few turns left to reach it, good things to bulb along the way with Great Scientists includes philosophy & education which can really speed things up.
-) See how opponents are doing in tech and see how long you can postpone liberalism
-) Get the best possible tech from liberalism (steel is awesome [cannons] or military tradition [cuirs])
-) While teching to military tradition or steel, start producing troops, if military tradition, you can build and later upgrade war elephants, if steel, you should have 8+ trebs available for upgrading, and 20-30 regular troops (pikemen, macemen, longbows(?) & crossbows ready to attack one turn after you get to lib/steel).
-) As soon as you hit your target tech with help of liberalism (Military Tradition or Steel), go ALL OUT WAR! Turn slider off, whip a unit every 2nd turn (except for capitol) and declare war on a juicy target, conquer him/vassalize him and do the same to the other guys.
-) When AI catch up to you in tech (reaches rifles/cannons) you might need to reach the next unit type that is great (infantry & artillery). Delete/gift most of your units and start researching again.
One of the key concepts of Civ4 is to min-max, what this means is to when you decide to do something, you go ALL OUT towards that thing. If you tech, focus on teching (build wealth), if you war, do nothing but produce war units. During early phases, you should focus on expanding and reaching a good tech that allows you to expand more (Currency/Code of Laws - Courthouses). The earlier your land and new cities are developed - as long as you can afford it - the faster you can do stuff later since you have more powerful cities/more methods to help you.
MinMax also boils down to city specialization, if a city produces many coins (riverside grassland), improve it by adding a market/library and more cottages, dont try to make it into a GP-farm and producing coins, and lots of production, if a city can work many hills, build farms and mines and make sure it focuses on producing hammers and add production multipliers.
The MinMax also applies to gaining momentarily advantages, if you reach new war units that will give you an advantage and some opponents don't have a counter for it and cant reach it for a while. Use that advantage to produce massive armies (whip, whip, whip) and crush them to increase the size of your land and then rush on to the next tier of war techs.
Early phase (claim land and get to the juicy techs): Expand to 3-5 cities claiming some decent land that will help you reach currency/bureaucracy techs (get some strategic resource for protection [copper/iron/horses])
Next phase (start generating science): make your capitol a SCIENCE CAPITOL (cottages, improved by nearby other villages that has helped you develop them, produce a Great Scientist in one of the other cities that can help you further improve science generation in capitol)
Next Phase (win the race for liberalism): Get as much happy/health resources as you can to further expand your capitol and thus science creation (trade for happy resources and health resources, place cities on or near those resources, get monarchy and place garrisons in capitol)
Next Phase (dominate): Go into war mode [turn off slider, whip units, conquer AI, vassalize them if you think you can take on someone else earlier due to this]. And then win...
When it comes to war techs, these are units that work great and can allow you to be in an advantage if you reach it earlier than opponents are able to counter them:
- War elephants & catapults (if you need to do an early rush [attack before they have too many longbows])
- Cuiraisers (fast moving unit which is fairly strong and easy to reach, [attack before they have rifles, best for "breakout" wars that allows you to take out 1-2 nearby opponents and then tech cavalry])
- Rifle/Cannon (good combo that will keep you going until AI reaches infantries, but very expensive to tech both, thus cannons are better to go for if you can lib steel and combine it with general land troops since nothing counter those before cuiraissers/cavalry)
- Cavalry (awesome if you have cottage heavy land, you will probably want to lib communism and build kremlin and then rush buy cavalries with 0% tech slider (requires A LOT of techs and cottage cities to be effective)
- Infantry/Artillery (works against pretty much anything, you can most likely keep producing these even if opponent has tanks and stuff)
- Fighters/Carriers/Battleships/Marines or Infantry (works against almost anything on a sea based map where your fighters on carriers will reduce all opponent units to half their strength, watch out for massive submarine spam though and beware of tanks)
Well, these are the basic rules that apply to almost any difficulty level and most of the games. Other than that, produce workers (you need to work improved tiles, otherwise you are playing inefficiently), use the whip - high population costs money and unless they are working awesome tiles with good multipliers they usually aren't that useful. Don't build random crap buildings or wonders. Do build courthouses if you need the money and can avoid the x turns it takes to build them.
When you produce wealth, make sure you are still working "hammer tiles" since they are moved away from these tiles if you have "automate citizens" on.
And most important of all, ignore what I just wrote, Civ4 is a strategy game and there are no "guides" to how to play it since every map is random and every game on the map will be different. By playing a lot, you will realize what works and what does not work for you, with your personal playstyle in a way that you think is fun on that specific map.
