Try this recipe and see how it suits you.
SETUP
1) Prince, pangea, speed normal/epic/marathon, everything else as you like it.
1) Choose any/random leader
FIRST STEPS
2) Research mining (if you don't start with it), bronze
3) Your starting scout/warrior looks to find nearby civs. You don't need to actually see the cities, but you should know where the nearby civs are. You can tell by color which civ they are. Secondary aim is to pop huts, but scouting is the most important.
4) Build a worker if you start with mining, a warrior if without (the goal is to get your worker to be ready within about a turn of researching bronze working
5) Get your capital to size two. Build a warrior if you still have scouting to do. Start a barracks if you don't, but switch to worker when you reach size two.
6) Chop down forests near your capital with your first worker to get a second worker.
DECISION POINT
7) Big question: where's the copper? You need to hook it up ASAP. For the purposes of this exercise, restart if you don't have copper within 10 squares of you capital. (I don't recommend this generally, but this is a specific exercise.)
8) Second warrior does scouting if first scout/warrior got killed. Secondary duty is keeping the fog of war clear around your copper site.
9) Chop a settler with your two workers.
10) Get that second city set up so that a) you have copper, and b) it has a good mixture of food and production.
11) While waiting to get the copper hooked up, build barracks in one or both cities.
12) If you have a barracks in your capital, build warriors. This will let the city grow and provide garrisons for your first few cities.
13) Once copper is hooked up, make sure both of your cities are connected by roads
WAR PREPARATIONS
14) At this point you should have two cities with barracks, two workers and a few warriors. Make sure there is at least one warrior in each city to keep the people happy. It is time to build up the troops.
15) Chop another worker if you have lots of trees.
16) Set your cities' citizens to work tiles so that the cities will grow as quickly as possible to maximum happy size. If your happiness limit is 6, you want to get to size 6 as quickly as possible, but you don't want to grow to size 7. This will mean that you will switch from food to production (hills, forests) tiles. At max happy, stagnate your growth.
17) Set both cities to produce axemen. Chop forests. Use axemen and extra warriors (if any) to protect your workers from barbarians if outside your city borders.
18) After you've got bronze and roads, your research goals are a) worker techs for any nearby resources (agri for corn, animal husbandry for pigs, hunting for elephants or deer, etc.)
MARCH TO WAR
18) When you have 8 axemen, it is time to attack. Pick your target. Your target civ is the one with its capital nearest your cities. You should know who this is because of your scouting. Tiebreaker: Choose the civ with the best looking cities over the one that's surrounded by deserts or jungles.
19) Group all your axemen together as a single stack. Do not promote them yet.
20) Use one of your two workers to build roads to the enemy territory
21) Use your other worker to improve the production capacity of your capital
22) Build another worker in whichever of your cities can build it the fastest
23) Other than this third worker, build nothing but axemen in both your cities.
24) Use your workers to build a few mines to maximize production. Then, put them to work chopping out axemen again.
25) March your 8-axeman stack to the nearest city of your target civ
26) If you can attack a worker of your target civ, this is ideal. Then you don't need to build a third of your own, or you'll have an extra.
27) Continue to produce axemen in your two core cities, but also improve the land around them
ATTACK
27) You are now at the outskirts of the nearest city (to yours) of your target civ with a stack of 8 unpromoted axemen. Their city is defended with two or three archers. You are standing on a forested/jungled hill, in a forest, or on a hill if at all possible. You are not standing across a river from the city!
28) If you are aggressive, your first promotion will be cover (bonus against archers). If you are not aggressive, your first promotion will be city raider (CR). In any case, each subsequent promotion will be more CR.
29) Promote each unit as it prepares to attack--but only if it needs it. Check the attack odds by holding the right mouse button down but not releasing as you target the enemy city. If the odds are above 95% (because the archer is wounded having killed one of your axemen), do not promote before the fight.
30) Take the city. You might lose a few axemen. Mourn them briefly while the core cities train more to replace them and send them this way along the roads your worker is building to support the assault.
BRIEF REGROUP
31) You want to have at least 6 fully healthy axemen before moving on to the next city. If this means you wait until reinforcements arrive, so be it. Wait with your troops in the newly captured city while the resistance settles down so you don't have to pay unit support costs.
32) Don't let your workers get killed
33) Expect a slight counterassault from the enemy civ, perhaps toward your core cities if they bordered you with two cities. Absorb the counterassault with troops fortified on defensive terrain. If they send lots, promote to woodsman and maybe have two units defending.
34) Promote wounded axemen the first turn after the city attack. This will shorten their healing time. Since they will have had 4 exp from the barracks, a single successful attack will earn them another promotion. Choose the next city raider promotion for them.
35) When you have 6 fully healthy axemen, move on to the next city. I doubt if the AI will have more than two cities. (Wait until they are size two before attacking, otherwise, they vaporate.)
36) Leave your weakest axeman in the city as a garrison. It's okay if he's still healing.
37) Keep churning out axemen in the core cities and sending them to the front. Use captured workers to chop barracks and axemen in the new cities.
CONTINUE
38) If you did this quickly enough, you can repeat with another civ. It may have more cities and more defensive troops, but you have promoted axemen and more production capacity which will more than compensate.
39) Note that the AI likes to send out archer/settler parties even as you're laying siege to their cities. Engage them on open ground, and it'll be mostly free experience for your troops and a worker for your empire.
40) When you reach about 6-7 cities total, you will need to stop and concentrate on the economy for a while. Get some workers out there improving and consolidating your empire. Put extra troops in your cities that border aggressive neighbors, but they will likely respect you enough to attack someone else.
NOTES
41) You will likely be in a much better situation with your new 6-city empire than you would have been by founding 3 cities of your own.
42) You can now be a builder for a while. Put up some city improvements. Pick a religion from among your captured cities.
43) Research your way to pottery, alphabet and then to construction and iron working. Get some cottages down to pay for your fabulous empire. Maybe do some tech trades.
44) When your economy is taking off, it's time to start thinking about the next war. Put together a couple strike groups of 5-6 catapults, 4 swordsmen and 2 axemen and pick another civ to conquer. Choose the nearest one with a high score. AI score tends to go to the civ with the best land, and that's the land you want. The nearby cities will cost less to maintain. The pyramids are nice to have, so you might want to conquer that civ if it's convenient....
END NOTES
45) You can continue warmongering if you like. Or, once you're above double or triple the land of your nearest competitor (check the demographics screen), you can be a builder and win that way.
46) There are many modifications that you can play with here. What happens if you don't have copper? What if you are Incan and want to rush even earlier with once city and quechuas? But the point of this recipe is to develop a taste for rapid expansion where the cities are founded by the AI (or barbarians) instead of by your settlers.
47) Continents and especially isolated starts are another ball game, but the skills you learn by cooking this recipe will help.
48) Land=power. Power= more land. Better land sooner = More power to ya!
ENJOY