This post may be a little, but I just found this forum so you'll have to forgive!
I like Arrian's post very much. For the most part, that is the strategy I have adopted...
My main focus in the early game is getting warriors out to explore for many reasons:
1) I can send the settlers to regions I know have serious resources that will jump start my cities.
2) My warriors can make contact with other villages, getting either a science, military unit (to do more exploring) or even a settler...
3) Meeting other barbarians and killing them for sometimes 25 gold or 50 gold and in the process, making an elite out of the warrior
4) Meeting the rival AI's early in the game is good because they often want to trade sciences, and I just do counter proposals and give them cash from the dead barbarians instead of my science.
Now, you're probably thinking, how the hell do you do that with a unit that only moves a single square at a time?
Well, here's the trick, take it to the mountain! The warrior travelling from hilltop to hilltop can survey an incredible amount of space.
During your exploration, your initial worker needs to get to work. His initial moves and roadbuilding can also have a significant effect on the long term. I think that it is worth the effort to build a road to a luxury, even if it's in the mountain... But if there are no luxuries in plain sight, then the worker should focus his work on plains so that he can build roads faster.
Usually, I build the road in spaces previously explored by one of my exploring warriors. My first city builds three warriors: the first two go and explore, the third stays behind to guard the city. If my city is at population 4 after the third warrior is built, then I build my first settler, otherwise I recall the worker to increase the city's production.
The first settler get's no escort because by the time he's off to build a city, one of my exploring warriors is one his way back, to pass through and he'll take on any wandering barbarians. The second city will first build a 1-warrior, 2-temple or barrack and the worker should already be working on a road for the third city. If the second city grows rapidly because of the choice location and the mines and road already in place then after the city improvement, both the capital and the second city should be ready for settler production.
If I've met an AI already and he's not to far, then I would get the two settlers to go near the AI's border to settle there, for two reasons:
1) I'm creating a border with the AI and chances are he'll start expanding in the other direction, so I'll be able to settle the rest of the spare space at your leisure.
2) Later in the game, I can build palace in those bordering cities and chances are, the AI's bordering cities will want to join me.
After I've established four cities, there isn't another city established without a warrior or archer for immediate security and city happiness. I try to build as many wonders as possible too. The first two wonders are usually built in my capital city, after I build a second worker... The second city may also build two wonders... But it's not impossible to get more than half of the wonders completed.
My general rule is, until the date is 0 A.D. I try to expand aggressively, after 0 A.D. I need to work at seriously improving the city, roads, irrigation, mining, the works.
I don't worry too much about the time it takes to research new sciences because most of the time, I can just buy them and they're not expensive at the beginning of the game. Once I notice the AI has no more sciences for me to buy, then I pay more attention to sciences I pick. But I only start accelarating research when I'm in the middle ages.
Anyway, I feel I'm telling my life story here... This usually get's me off to a good start, sometimes a great start!
Good luck
Xenzat