I'm by no means good at this game, but I can beat a moderate enemy handily. Here's what I'd suggest.
Pause. Pause all the time. RoN makes it devilishly easy to forget things. By pausing and taking stock of your nation, you can spare yourself the horrors of forgetting key upgrades and paying for it in the amusing screams of your loggers when the dragoons come calling. Build towers near your vulnerable citizens and research attrition in them. Militarize before you need to and maintain at least something of a standing army. Keep a cavalry in a centralized position so that they can race to the defense of any quarter of your nation.
Focus on key upgrades, like taxation, and remember to build resource upgrade buildings like granaries and lumber mills. You don't neccessarily need every upgrade they provide RIGHT NOW, but just having them boosts resource collection and helps your economy hit the boom point, when you can crank out troops like an ant farm.
At the library, do Science first and wait till it completes before picking others. This is because, once the Science upgrade is complete, the others are reduced in cost. Also, don't do what my wife does, which is to keep building farms while you're at your food commerce cap. Again, pause and figure out where citizens are wasted, and where they're needed.
In battle, I can help you through the enlightenment. The key to enlightenment battle is to have strong, orderly skirmish lines. (you may want to turn on advanced options and set foot soldiers to STAND GROUND.) The Game does a great job of approximating how battle actually worked in that era. The infantry lined up and hammered away at each other. Then, separate from the infantry/artillery corps, the cavalry attacked from the sides and rear once the enemy army was engaged full force, knocking out artillery, supply, and command. It's a bit simplistic for fights against other humans, but it will give the computer a good drubbing. Also, in the enlightenment, you'll want two musketeers for every fusilier. It's more complicated earlier on, and you should tailor your force to your enemy based on how they have attacked before, or what nation they are. Expect horses from the mongols, and heavy soldiers from the Romans and Japanese, etc.
"Years from now, do you think a bunch of geeks in a game forum will be quoting my work?"
-Sun Tzu