I have been playing continents/emperor. I generally try to take control of my home continent with horsemen, beeline for caravels, while I cover my continent with cities and pumping up the science. From there you can either take the easy Spaceship win or go for the more difficult Domination win. If you're going for Domination, at some point you take most of your science specialists out and have them work gold.
One big variable is how many civs are on each continent. Usually it's two continents with 3 civs on each. One civ will typically dominate the other continent and you will be in for a difficult invasion. I have seen 4 civs on one continent and 2 on another, and even a 3-2-1. When you are on the 4 civ continent wiping out 3 other civs with horsemen is a lot tougher, but you can coast to victory easier once you have. The real challenge is when you are on the smaller continent with 2 civs and there is a dominant AI on the continent with 4 civs.
Naval invasions of a mature and powerful civ are difficult things. I try to create a zone of death on a beachhead with battleships/bombers/stealth bombers and hopefully some technologically superior units. Most often I beeline for Mech Infantry and use them (until Giant Death Robots come along) because I want to spend my oil and aluminum on ships and aircraft. (If you can, plan your landing near cities with strategic resources and take them first - but I wouldn't sacrifice a lot of distance from the homeland to do this.)
During the invasion you want to use good tactics to preserve your units. Don't overextend them, end turns on hills, etc. I find that taking out artillery when you see it so they can't gang up on a single unit helps a lot. I would guess you want to kill 5 or so units for every one you lose. After a while, they just sort of stop coming and you win.