Just had a go at this and I sucked TBH
What's the best strategy to roll with at the start? Build as many Settlers as possible? Should I attack the other civilisations, or wait until later when I have cannons and stuff?
No. (Once you get the hang of it you really need to war from axemen onwards, but lets cover basics..)
Build far too many cities before your economy is growing you will end your game quite quickly. You won't be able to research or build much, and the AI opponents will start to dramatically outstrip you in the turns to come.
Don't 'accept' a map or game if the area you are first presented with has no food resources. (Go to the options and hit regenerate map if it looks crap)
You ideally want two to three food resources in the 'fat cross' of your capital, and anything else on top of that like elephants etc is just a bonus.
Scout out the map to start with regardless if you are starting with a warrior or scount... just leave your city empty - no one will touch it. I actually tend to send out the first three units I build as soon as I build them to go hunt land and huts. The more land you map out the more 'huts' you will find, and hopefully get a few bonus techs or units.
Once you have your capital city to a population of around 3, either build a worker to improve terrain or go for your first settler. this depends really on what the land immediate to your first city looks like.
If you can see another 'sweet spot' for a city, I'd maybe go for settler first. If all the land is average, I'd maybe go for a worker to improve your capital then build a settler.
You need at about three workers by the time you have two - three cities as a rough minimum. Just to get work done at a decent rate, you can use them each on their own or group all three and get one job done quicker. Depends what you 'need' at the time.
When building your second and third cities, what I said about 'accepting' a location with regards to food sources for your capitol applies. They really need to be built near food to allow rapid early growth.
Try to ensure that you can keep your research slider at above 40% ideally when you are expanding (each new city is an added cost per turn), try not to let your economy get worse than this or you will end up losing a lot of research per turn and you will probably struggle to dig your way back out if you do not have appropriate technology, like banks and courthouses etc, to generate more money to ofset your increasing upkeep.
Having a lot of military units as well costs money in upkeep, so try to keep a balance between being overpower and underpowered.
At this point you should have Bronze and Iron Working by now (it is a good idea to try to get them sooner rather than later), and if you are unlucky enough to have these metal resources appear outside your land - this is your only priority now or your game is as good as dead.
Expand to take the metal and mine it (or just mine it if it appears in your own land), build a quick army of Axemen. If you have horse build a pasture with animal husbandry and make chariots etc You can also use your workers to chop wood, this will speed up production of whatever you are building in the nearest city.
This is helpful if you need an army quick, or are trying to 'rush' complete a particular world wonder - like the great wall.
You now have a mini empire (hopefully) of three medium sized cities that should growing at a steady rate. A small army to defend, or to go rush attack any poorly defended cities you may find nearby.
As a rule of thumb, always accept open border offers. You can scout out enemy land and see if you may be able to rush and overpower them early on if you have managed to get your resources and cities in good order quickly.
After that, try not to expand too quickly.
It will probably take you a few tries to start getting the hang of it, so in the mean time I would play it on the lower difficulty settings.
Head over to civfanatics for some good articles or ask if you need specific help with anything!
Oh and the best bit of advice I can give you, is read the manual if you got the retail.. or try to find it online. It is actually quite comprehensive in detailing the various components of the game.
