It's really not that difficult. Build transports and station them in a couple port cities, I usually use 2 cities. Try to have about 6-8 transports in each city, and stock them with a variety of units. Make sure to have some armor, along with infantry (i.e. marines). You want to have something to protect the transports, so send some destroyers/battleships/submarines (I tend to go with submarines). Try to choose a good landfall point, somewhere with lots of space. An ally's territory is perfect, that way you can re-organize your troops into stacks. Also, try sending aircraft to your ally's cities to be stationed there for when you attempt to take a city. Always go in with planes first when trying to take a city, while doing this use a unit like a tank to destroy surrounding improvements (ESPECIALLY IF ITS A MATURE CITY). If you have ICBM's, all the better. Just fire them off then ransack the cities.
While doing all of this, send your naval fleet back to your mainland to restock them. You'll never take out a whole country without shipping in reinforcements, and try to keep teh reinforcements diverse. And when going across the ocean, obviously keep your ships in a large stack. That way if you're attacked in the sea, you have an opportunity to retreat and salvage your units. And make sure you have a solid sea defense, with good units guarding the waters. I started a war like this once, and never took that into account. The AI sent destroyers over and blocked trade routes, causing my cities to starve and i couldn't produce any more land units or naval units to get red of the AI destroyers. Because of this, I had to end the war.
Don't rush into it unless you like losing, make sure you're prepared. Another wise idea is to get a close ally of yours that neighbours the enemy to cancel all deals with that enemy. By doing this, you create a "home away from home" for yourself. If you have an airport in your cities, then you can quickly fly units over to the ally, and place air supports there.
So in summary, create transports with some extra firepower, stack them up and send them to an ally of yours thats neighbouring the enemy, send air units and weaken the city of your choosing, then take them over one by one (if its under level 10 just raze it). Keep a solid naval defense and keep shipping units over. Make sure to send the transports in stacks with other ships and send them over in a straight line, ignoring other ships. Have fun.
