Program for World Domination:

Step 1. Open the science report and set your science goal to Monarchy.
Step 2. Set your science rate as high as it will go (60% in recent versions).
Step 3. Move your Explorer first so you get as much information as possible. Use your other Settlers to build two cities about 4 squares apart. Set each of them to build more Settlers. When you get close to completion of one of them, buy it. You need to grow *fast*.
Step 4. Meanwhile, use your Explorer to explore. By hand. Try to move outward in an expanding spiral. Enter all huts you find ASAP. If you lose your Explorer to barbarians, you'll just suffer a little more, but it's worth the risk.
Step 5. Whenever you build a new Settler, use it to build another city about 3-4 squares away from your growing empire. Then have that city build a Settler. Use any gold you pick up from huts to finish building Settlers.
Step 6. About 1-2 turns before you research Monarchy, stage a revolution. Even under Anarchy, you still pick up 1 light bulb per turn per city. Ideally you want to learn Monarchy right before the end of the revolution. If your revolution ends too soon, start another. Become a Monarchy. Monarchy is the best government form in the whole game for city growth, because you don't suffer the food penalty of Anarchy/Despotism, but your Settlers still use only 1 food per turn. Your people will now gorge themselves and breed like rabbits, especially near fish/game. Later you'll be irrigating, of course, which helps even more. Once you've learned Monarchy, your science goal is up to you. It depends on your style and/or situation. Try to pick up the Republic, Trade, Seafaring and/or Invention. Set your science rate to the maximum.
Step 7. Once you've got about 8-10 cities, you can turn your attention to Wonders. The Pyramids are the best wonder to start with, since they'll double your growth rate. If you get Trade, you can accelerate wonder building with Caravans. Build roads and irrigate a few spots.
Step 8. If you're on an island, or lost your Explorer, then you'll want to focus on naval technology early. Get Seafaring, and then Steam Engine within a reasonable time frame. Ironclads really ruin the AI's day early in the game. Seafaring builds from Mapmaking, so you'll have Triremes for exploration and possibly transport. It also allows Harbors (more food = more growth = more power) and a replacement Explorer or two. Put one of your explorers on the nearest arctic spot and let him walk around the world, picking up any huts. You want to do this early, though, since the AI will build cities in the arctic zones, and your explorer could be endangered.
Step 9. If you're on a continent with AI opponents, then you'll need to eliminate it/them. This demands a rather different early strategy (and is much more difficult, since this is where the AI does its best work). Shift your trade balance away from science and toward gold. Build diplomats and your best defensive units, and some good offensive units. If your enemies have lots of coastal cities, you can pound them with ironclads. Even if you don't ferry land units over to occupy the enemy cities once you've killed all the inhabitants with ironclads, the AI will still panic, and build more defenders in the city, which you can continue to kill off. (Of course, only attack if you easily win the battles, and never with a damaged ship. The idea here is that you lose nothing; withdraw damaged ships to your nearest city so they can repair themselves faster and then kill more enemies.) If you have to fight overland, then draw the enemy out. Fortify defensive units on mountains, hills and forest, to hold the AI at bay, and to provide cover for your offensive units. Pick off any enemy units that offer themselves (exposed catapults, etc.). Buy a few enemy cities with diplomats. Don't rush. Once you control your continent, you've basically won the game; the next 3 steps are just mop-up.
Step 10. Don't forget to keep growing, although you can slow down after a dozen cities or so (depending on how crowded the map is). Expand onto nearby islands, including arctic outposts. Shift to Republic once there's no danger of enemies conquering you overland and you've got temples in your larger cities. Let your people have some luxuries, and build trade routes. Build up a treasury. Stockpile a few diplomats; they have no upkeep.
Step 11. Focus on naval technologies. Get Amphibious Combat, and build some (veteran) marines. Build good (veteran) combat ships and some decent transport ships. Build Leonardo's Workshop early, so your units will be upgraded for you. Don't learn automobile. You can learn *rocketry* without automobile. Build Magellan's, and if the lighthouse is still available, build that. Don't be the first to learn Magnetism if you've got the lighthouse. Your attack fleet will now consist of one transport, at least one marine, and as many warships as you like. (By now, cruisers are probably best, so work toward them; settle for destroyers as long as they'll work.) Use your warships to empty an enemy city you'd like to own, then move your transport next to it, and unload one marine who can walk straight into the city and take over. Then move the transport and at least one warship in (even if it's wounded). On the next turn, sentry the marine, which puts him on the transport for free. Use your warships to empty another nearby city, then move the transport over and let the marine (the same one!) conquer this city. Your warship is defending the one you just took while it repairs itself. At this point, the AI won't retaliate, though, since it's now scared to death and is trying to put more defensive units into its cities. Which you're about to take. When you feel ready to move your occupying warships out, you can let the occupied cities build defensive units of their own to take over that duty. But you won't need them for long; if you take over that continent/island soon enough, you can leave the cities undefended. Whenever you see an AI ship, sink it, especially if it's carrying something (has a '+'). If you rule the seas, the AI can't get anywhere near your undefended cities on your home continent. You won't be letting the AI survive long enough to pick up flight.
Step 12. For variety, especially if you just took over an enemy capital, you can buy enemy cities with diplomats/spies. Spies are better at this, of course, since they sometimes survive. Be sure to "home" the spy to a nearby city of yours so it comes back right on the front lines. AI cities are a real bargain, and sometimes you pick up lots of perfectly good defensive units and maybe a ship or two for next to nothing. And Leonardo will help you upgrade them.

There are omissions here, of course. I'm sure you can figure out what goes in the gaps.

From Freeciv, a Wikia wiki.