I'm going to assume he doesn't have stealth fighters yet. And while I agree that MY preferred course of action is just show up with some dips/spies and alot of cash to take AI cities... the post is about how to win with military (I think
I'm going to assume you're playing 1x movement also.
What I would do is:
1) send in dips to at least knock down city walls.
2) fortify a rifleman or similar unit on good defense terrain, and either hope the AI wastes any offense units trying to kill it, or use it to protect movement 1 units like catapults, cannons, artillery or whatever you've developed. The additional advantage is that you can use that unit to defend the city once you capture it.
3) send a mass attack from all sides on ONE city, KEEP it, buy city walls if you can the FIRST turn, fortify ALL your units in it. Sell the useless and most expensive improvements first (i.e. university, bank...) And for all you people who say, WAIT, THOSE arent useless, id rather have the cash now in an a captured city on the front line, and in case its recaptured (although it rarely is) you lose em anyway.
4) Buy new units or move more units into THAT city, and use it as a stronghold until you're ready to take the NEXT city, and repeat process.
Eventually you'll wear your enemy down and your forces will render his seem laughable. When you have completely secured the front, and the war is won, you can concentrate on integrating the captured civ into your own.
Remember the first couple of cities are usually the hardest, and soon enough they start falling like dominos (this principle works for multiplayer as well as solo vs. AI).
Any further questions? Ask 'em here or find me at night on the MSN Zone (Civ II MGE, of course!)