I have found that war is a must for 4X games. Even if you don't start one yourself, some one else will. Hope for the best, prepare for the worse.
You can set yourself up for a defensive war, but depending on your government type, that might not be an option. With govs like democracy, war wariness hits hard and very quickly, so you have American style Shock and awe to end the war quickly and decisively. Basically blitz at least half most, if not all your opponent's cities in ten turns. It requires you to expect a war with your neighbor so position your guys along it. Concentrate most of them in one or two cites depending how large your army is. Then wait for war. Aircraft is a must for intercepting guys making a run for your cities, but those are few. once you knock them back into the defensive, that frees up aircraft to soften retreating units. The bulk of your army should be doing a smash and grab of the cities. If your fast enough, you can out run the defenders and take cities almost undefended. Having aircraft carriers off shore is great for opening up another front to draw off troops. Off course this is all modern age if tanks and mechanized infantry. Forget about artillery, not worth the time or damage to units or cities.
During all this time make sure that your entire nation is mobilized and cranking out units. Some are lost replacement, but most are for garrisoning since that places your taking aren't very happy about it all.
Unfortunately Civ games and especially civ 3 are not very conductive of world domination. It is mathematically impossible to achieve as your nation very easily falls into civil war past 150 cities. The empire size penalty is just too great to compensate for. I have seen A.I.s approach 200, but they are so weak internally, they fall over to a light breeze. Also having overseas holdings isn't worth anything as they are so inefficient, they drain resources as a whole. You pretty much have to burn down most of the world to gain the world domination victory.