Best way to win an early war without falling behind in technology, is to have offensive units doing routes around your cities to make sure the enemy does not pillage your improvement tiles. Always keep a couple of units laying around with +% against Catapults, and +% against Mounted Units so they can make quick work of those highly annoying Catapult/Longbowmen, and Horse Archer pillage units that the AI likes to throw your way.
There are other factors that will limit your technological growth however.
- Making more units than your gold surplus, forcing your technology slider to decrease to compensate.
- Taking too many cities, forcing high maintenance costs, forcing your technology slider to decrease to compensate
- Losing possible trade income from the allies of your enemy.
- Letting enemy ships reach the coastlines of your coastal cities; there by forcing starvation on your city as you can no longer work the sea tiles.
The trick to successful warring is not to force yourself into a prolonged conflict to the death with your enemy. Instead try taking a city or two, pillage his capital improvement tiles, then call peace on him within 10-20 turns. The damage you've done to his economy is insurmountable. You can also bully this nation for the rest of the game, or until you're in the Industrial ages and ready to dominate/conquer the world.
I personally like to form early-game alliance blocs by forcing my religion onto other nations; or by adopting the most favored religion out there {Usually Buddhism on Pangea maps.} This makes you the good guy. Then declare war on a "Heathen" religion, and start calling the people of your religion into war against this person. This gives you, +1-+4 "The struggle against our mutual enemy brings us together", which will last just long enough for you to sneak in some good tech trade deals if you already have the Alphabet. AI's are more willing to give up techs if they trust you. Just remember not to finish this particular nation off even if you're ready to strike a final blow on their capital city. Instead keep them around so they can remain the common-enemy for your Alliance Bloc.