I would reccomend reading
EVP I: The Destructive Vikings. OK... end of shameless promotion...
Anyway, in that game, I had the same thing... a run away civ (in this case, Shaka), who had vassalised India, and ruled the entire continent.
My initial idea to "capture" cities was a failure. If the person has any half-decent army, any capturing of cities pre-flight will mean that you will have to constantly reinforce the city, until, eventually, he will get it back. Pre-combustion, it may happen after just 1 or 2 reinforcements.
What worked, however, was razing cities. Now, I was playing as the Vikings, which helped ALOT. However, if you can take some archers with you, you can not only take out all cities on the coast with a hills adjacent to both the shore and the city with ease, you can even take cities one tile in. Just give the archers insane Guerrila promotions, hold out for one turn, wipe out city defences with a spy, capture it with collateral damage, and retreat. You will have much lower losses than the enemy (as long as you pack lots of pikes for those pesky Knights, flanking your cats and trebs), and you can just keep on hopping around the coast, razing and pillaging cities everywhere.
Eventually, the damage done by the razing will give you a tech lead, and with that tech lead you can choose to either go for space race, or win by conquest/domination by getting more and more advanced troops to raze the cities.
An additional interesting thing is that, if you raze all the coastal cities, the 'new' coastal cities which would replace them would lack the vital infrastructure to build galleons, and thus they will be less able to launch a decent counter-attack.
Just one thing... from previous games, NEVER let the run-away civ survive. At least cripple him so you can win time...
If you are playing a game where some civs (no matter how weak) still are alive, befriend the surviving civs, and fight for 'their' freedom. Use their land as a landing beach to take over some cities. Also, try and bribe them to join war ASAP, as you will need them to defend you from counter-attack until you have a strong beach-head. They will likely be weak from the wars, so giving them techs to help (preferably military techs) will help even the score on that continent.
[Edit] Or use Joshuas tips, where you blow up the weaker civs, and use those places as a beachhead. Just check that they haven't already vassalised[/Edit]
Whatever you do, you MUST destroy the civ's infrastructure. Either by razing the cities, spying them to death (unlikely and expensive), or capturing the cities (only advisable if you have similar military powers, and/or flight, and/or playing as Vikings with transports for rapid reinforcement)
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