As has been pointed out, the term "early war" is fairly relative, so for the sake of discussion, I'm going to define it as a war that occurs within the first 30% of the game.
Now, here's the types of wars available, as I see them:
1) Early Raid - This occurs while you have just Warriors. The point of this type of war is to harrass your neighbor, not take territory. Your primary goal is to slow the neighbor down, and make it difficult for him to expand. Use your warriors to pillage improvements, and if possible, capture a worker. If a settler is sent out, try to kill it and it's guardians. If possible, draw your rival's bowmen out into the open, or get them to attack you on hills/forests. In the mean time, you should be getting your own second city out, at least one worker, and in between building more warriors. You're also going to want to prioritize a tech that will give you a distinct military advantage.
The downside is that you won't be grabbing Stonehenge and probably won't get the Great Wall. The upside is that you've weakened your target for Stage 2.
2) The Axeman rush. As soon as possible, get 1 worker, 1 settler, bronze-working, and the ability to either build roads or transport across goods across water. Obviously you're going to be settling your second city next to the nearest source of copper. If there's no copper available... oh well. Settling 2 spaces from the copper is a bad idea, unless your leader is Creative. Even then, I wouldn't recommend it. Mine the copper and connect it to both cities.
Start building axemen in both cities, and as soon a city is both size 3 and has no unhappiness from using the whip, whip again. If you have a food improvement tech, try to improve a food resource at your second city. If you have multiple workers, try chopping trees at each city. If you have a barracks, that's a bonus, but don't prioritize it.
As each Axeman is built, send him out to hunt barbs and gather XP. Keep one or two near each city as by this time you'll probably start having to worry about them attacking you. Once you have your attack force prepared, build two more axemen to leave behind as defenders. THEN you may go on the attack. Ideally you're going to be pumping these guys out every 1-4 turns (depending on game speed and resources available). The size of your offensive force can vary. No less then 6, and I generally send out 8 with reinforcements being built. 4 can generally take out any plains city w/out walls. A highly defended hill capitol is going to generally be unassailable unless you've build a force of around 10 guys PRIOR to declaring war on your target.
3) The Zap Brannigan method. This comes after the ideal time for an Axeman rush. You'll probabbly have Swordsmen as well as Axemen, and possibly Spearmen. Your target will have mixed forces as well. The strategy here is simple, build a huge Stack-Of-Doom and overwhelm him. If he has 4 archers, well my 20 units should be enough. You will take massive casualties, and you probably won't wipe him out. Select 1-2 cities to raze/capture, accomplish this goal, defend against the counterattack, then declare peace. Rebuild, and Repeat.
4) Combined Arms. Basically, at this point you're using catapults along with Swordsmen, with some mixed defenders. This works best if you use the Oracle to rush Metal Casting, build a Forge for an engineer, then Light Bulb techs for catapults. Use the catapults to soften the defenders, then attack. You might also be using calvery to weaken the target's infrastructure, or spied to weakend defenses.
I usually build ten swordsmen, five axemen, and three catapults. And usually, the swordsmen are the only thing that ever make a difference. With my stack ready, I can usually take down ANY civ before A.D. So I think that swordsmen are highly underrated.
Sorry if I offended anyone.
?
