This is what I do: (worked very well at "monarch" level)
I usually play very aggressive; I try to wipe a civ in the early age, just after the first mounted units appear. They retreat when in trouble, fast and great in attack - they are my favorites.
I gather about 7 or 8 and then I start my concentrate attacks, training continuously at least another mounted in my cities. (I usually play with Militaristic nations). If you are in war most of the time you don't have to worry too much about the wonders... great leaders will appear pretty soon and you can build a wonder in one turn. Great Library is a must, also Leonardo's WorkShop, J.S.Bach, Hoover Dam; always buy or exchange techs, never sell.
When a civ has lost the capital or lot of cities, ask in exchange for peace techs, cities, everything you can grab; than attack again, sometimes after less than 1 turn.
NEVER attack more than one civ. If possible make MPP with other civs.
Later in the game, if you want to attack a the civ next to you, which BTW could be more advanced than you, build a very large no of your best attacking unit (mounted if possible), place your soldiers on the empire's borders (ROP if possible) and smash it in one turn with all you have. Attack 4 of 5 directions and overwhelm him by number. Capture the capital if you can; split their empire in two; conquer as many cities that turn before they can retaliate; hunt down all the attack units they might have outside the cities; don't pillage - you're going to need those improvements soon, when they will be yours; if a conquered city has temple or some culture improvement, destroy it!!! it gives culture points to the original civ; put to rest your harmed units in the your new cities - they won't defect that turn; later on, leave just one defending unit in the city, the cities will defect, you can be sure about that. Have no mercy! Hitler style. Conquer all you can! Make peace, ask for all they are prepared to offer for it and attack again. Don't let them even breathe. Destroy the whole civilization otherwise the cities will defect.
If you are in permanent offensive, your units will become elite in no time and eventually some great leaders will arise. If possible keep the peace with other guys, especially with those which seem to be strong.
If needed, set on mobilization (don't tell me it's useless or smth like that). The cities that are already building smth they will suffer no change, but the others will provide you a large army very fast. Of course, when a city building a civilian improvement will finish it, you will be able to chose only a militaristic one until the mobilization ends.
Tip:
When your culture is pretty strong you can make a huge profit like this: build a new city close to your capital, or somewhere in the heart of your empire. Immediately try to sell it to other civ. You will get a pretty nice price and the town will return to you in few turns, impressed, of course, by your high culture.
Bug:
Attack one civ. Conquer some cities. When they will ask for peace, demand 999999999 gold per turn in exchange. You will get the sum right away. Declare war in no more than 3 turns, otherwise you will lose the money.
I did that and it works, but I did not felt much better. It all become to damn easy. You can buy everything can be bought, spy, set the luxuries to maximum or pay for a civ to go to war to another civ. It's a bug, but I'll never use it again. It's just not fair.
Hope I help.
I usually play very aggressive; I try to wipe a civ in the early age, just after the first mounted units appear. They retreat when in trouble, fast and great in attack - they are my favorites.
I gather about 7 or 8 and then I start my concentrate attacks, training continuously at least another mounted in my cities. (I usually play with Militaristic nations). If you are in war most of the time you don't have to worry too much about the wonders... great leaders will appear pretty soon and you can build a wonder in one turn. Great Library is a must, also Leonardo's WorkShop, J.S.Bach, Hoover Dam; always buy or exchange techs, never sell.
When a civ has lost the capital or lot of cities, ask in exchange for peace techs, cities, everything you can grab; than attack again, sometimes after less than 1 turn.

NEVER attack more than one civ. If possible make MPP with other civs.
Later in the game, if you want to attack a the civ next to you, which BTW could be more advanced than you, build a very large no of your best attacking unit (mounted if possible), place your soldiers on the empire's borders (ROP if possible) and smash it in one turn with all you have. Attack 4 of 5 directions and overwhelm him by number. Capture the capital if you can; split their empire in two; conquer as many cities that turn before they can retaliate; hunt down all the attack units they might have outside the cities; don't pillage - you're going to need those improvements soon, when they will be yours; if a conquered city has temple or some culture improvement, destroy it!!! it gives culture points to the original civ; put to rest your harmed units in the your new cities - they won't defect that turn; later on, leave just one defending unit in the city, the cities will defect, you can be sure about that. Have no mercy! Hitler style. Conquer all you can! Make peace, ask for all they are prepared to offer for it and attack again. Don't let them even breathe. Destroy the whole civilization otherwise the cities will defect.
If you are in permanent offensive, your units will become elite in no time and eventually some great leaders will arise. If possible keep the peace with other guys, especially with those which seem to be strong.
If needed, set on mobilization (don't tell me it's useless or smth like that). The cities that are already building smth they will suffer no change, but the others will provide you a large army very fast. Of course, when a city building a civilian improvement will finish it, you will be able to chose only a militaristic one until the mobilization ends.
Tip:
When your culture is pretty strong you can make a huge profit like this: build a new city close to your capital, or somewhere in the heart of your empire. Immediately try to sell it to other civ. You will get a pretty nice price and the town will return to you in few turns, impressed, of course, by your high culture.
Bug:
Attack one civ. Conquer some cities. When they will ask for peace, demand 999999999 gold per turn in exchange. You will get the sum right away. Declare war in no more than 3 turns, otherwise you will lose the money.
I did that and it works, but I did not felt much better. It all become to damn easy. You can buy everything can be bought, spy, set the luxuries to maximum or pay for a civ to go to war to another civ. It's a bug, but I'll never use it again. It's just not fair.
Hope I help.