So, I have played this game quite a while, and have a few tips for those who care to listen, and aren't quite sure what to do:
1) Offensive wars aren't worth it for quite a long time. Little land grabs and pressure with a few spearmen (especially if it can get you the middle ridges) *might* be worth it, but taking any enemy city will almost certainly take a very long time and use up quite a lot of labor and resources, as well as letting those who aren't fighting get an advantage (since they aren't building tons of troops).
2) Put your effort into growing your civ early on rather then military (and military buildings) if possible. Obviously you will need a military at some point, but the longer you can delay it the stronger your civ will be otherwise.
2a) If you just focus on growing (building farms, getting quarries/lumbermills if you need stone/wood, getting more labor), you will quickly outpace those who even put part of their focus on military. Its important to note that for most of the game the limiting resource is labor, and you should work as hard as you can to improve it. Eventually you will need a military, but if you have 15 labor per turn but no army, and they have 8 labor and a strong army, you will be able to grow your army fast enough to defeat them either way.
2b) Each population uses up 2 food per turn. When you have half your pop in food, you gain another. That means that a population on regular plains without a farm will give no positive benefit, and a population on a swamp/forest will lose you a net food per turn. It is for this reason that farms/granaries are *very* important, and allow you to have a net gain of food and thus gain more population. (Sidenote: River/Bonus food plains are very good, you should try to get as many as you can, since the bonus food they get you is quite significant).
3) Troops eventually become obsolete (a massive army of spearmen and pikemen is pretty decent early game, but eventually they will become completely outclassed by stronger troops) it isn't that big of a concern in a single war, but that massive pikeman army you buildup will probably be quite weak in 20 turns, especially against someone who wasn't fighting and used that time to build to to be able to get stronger troops.