Foreword: this guide was written when 1.7.0 came out. There have been many subtle rule changes since, but as an overall strategy guide it is as valid as ever.
First of all, we haven't been playing 1.7.x long enough to develop a *perfect* strategy, so this one isn't. :) This one is just adapted form the strategies commonly used in 1.0k. It could probably be improved upon. That's your job. ;)
The game is divided into several stages.
Initial Expansion Phase
This phase is the most critical. The first thing you want to do is build cities and explore your island. You want lots of cities. The name of the game is to tie down as many squares of land as possible. When building a city, make sure that you don't overlap onto one of your other cities' territories. You can see which squares are being used by a city by clicking on it. The map of the city and the surrounding area contains that city's territory. Keeping this in mind, try to keep your cities fairly close together. The further apart they are, the more difficult they are to defend and administer at this stage.
Tip: Try to build on horses or near fish.
Now that you have a city or two, you'll want to set the science rate as high as your government type will allow. Don't worry about the tax rate, since you won't be building any improvements to drain your cash; you'll be building settlers. Every city should be churning out settlers. The more settlers you make, the more cities you can have; the more cities you have, the faster you gain tech; the faster you gain tech, the faster you win. After you have built as many cities as your corner of the island will hold, turn the settlers to irrigating and building roads.
(Note: If the food production in a city drops to +1 from supporting too many settlers, and you can't rearrange people to increase it, then switch them to building temples. Unless you make contact with another player, don't worry about building military units just yet.)
All throughout this time, you have been gaining techs as fast as possible. What you should be shooting for is first "The Republic," then "Democracy," then "Railroad," and then "Industrialization." As soon as you get the republic, start a revolution and change over to a republican government. Cities operate much better under republics than they do under despotisms.
When you get democracy, you are equipped to go into the Second Expansion phase. This is accomplished by changing the government to a democracy, making all cities build temples, and setting the luxury rate to 100%. When you do this, all cities will immediately begin celebrating, and will grow at a rate of one person per turn as long as there is surplus food. When they've gotten big enough, set the luxury down to a reasonable level of 20-40%. This places you in the Second Expansion phase.
The down-side to this is that setting luxury to 100% means that your science research will all but stop. After your cities have grown, and you put science back up to 50% or so, you will again gain techs, but at a slightly slower rate. If you have done some exploring, and are not immediately threatened by another player, it can be a good idea to keep science at maximum until techs start to take too long to generate.
Second Expansion Phase
When you get your cities to a good sized population, wean them of their luxuries gradually and increase taxes. Once they're down to 30% luxury or so, put as much of the taxes as you can into science, while maintaining a positive income. When you get railroad, turn all your roads into rails.
Tip: turn every square used by a city into a road/rail, it increases that city's output.
Now is the time to develop industrialization, and military technologies. You should also begin planting cities on other islands, and do some serious exploring if you have not already done so. You need to find out where your enemies are. Go for techs good for ships, and try to build Magellan's Expedition. When you feel ready, go into:
Now you're building factories and power plants in your cities. You want to get as much production as possible out of each city. Pollution becomes a problem. Try to research "Recycling" as soon as possible, so you can build recycling centers. Once you've got all your cities going strong, you must build military units. (Note: If you come into contact with another player, you should immediately build a few attack units, and at least one defense unit per city.)
When you want to begin thinking about attacking someone, set science to 0%, and put taxes as high as you can without provoking disorder. Remember, money can build units too!
Utter Annihilation of Your Enemies Phase
This can happen at any time, but it's more fun with the advanced weapons.
Pick a relatively weak enemy, and send over a few ship-loads of troops. Take over his cities, and use them to build more units to take out the rest of them with. Show no quarter! To the death!
Repeat as often as necessary. ;)