I agree with expand, expand, expand!
BUT, you also need to get some defense in your new cities right away. If you have a lot of undefended cities you will get bullied around. But if you have at least one spearman defending each city and at least one or two offensive units (like Horseman or Swordsman) at each border, you will not get pushed around too much. The AI ain't stupid and will go after easier prey.
My initial game strategy. I typically play China or Egypt at Warlord to Regent level, but this works with other Civs I've played.
1) Build first city, 90% of the time on the first square provided. At *most*, move one square but if you don't settle in the first turn or two, you will be way behind.
2) Pop out a Warrior to explore
3) Pop out another Warrior, Archer, or spearman, depending on your tech. Use to explore and defend the capital
4) Your city should now be near a 2, build a settler. All this time your Worker should have improved a tile or two and is building a road to your next city location.
5) Send your settler off. What I build now really depends what it going on. Typically I build a barracks.
6) New City should immediatly build Walls, perhaps a Temple after that. Once it reaches a 2, start a settler. Each new city follows this pattern, getting lots of workers going as well.
7) Somewhere I have at least one production city with a barracks. This city should pump out the spearman to defend all my new cities.
8) Explore like crazy to find other civs and trade techs. I usually head straight for Literature, then Republic and buy/trade for everything else. Also, get someone farther away to declare war on you after you have an embasy with it's neighbor. Now sign a military pact with it's neighbor. You've just started a big war with the AI Civ's going at it. After a while, declare peace or just sit back. You don't have to actually fight anything if they are far enough away. This distracts the Civ's involved from building wonders as they have to build an army. Good stratagy that works for me every time.
9) Once you have your inner core of cities, found cities on what you feel your border will be. There will probably be some empty space in between, that's fine, fill it in later. What you are trying to do is put up a ring of defensive cities in key locations and choke points to claim as much land as you can. Keeps the AI at bay and allows you to fill in the gaps cause you can kick out the AI's settlers if you have your ring of cities protecting your inner core.
10) You must have at least one city on each coast. This helps any military campains later on. If there is a large inland sea, get a city on there too. Get at least one harbor up ASAP so you can get trade with other Civs as soon as you are able.
11) Be the end of the ancient era, you should be about done with your expansion, now just work on infrastructure, especially libraries if you haven't already, and produce some military units in between. Got to keep a strong military, even if you rarely use it. Think Ronald Reagan here. The best defense is a strong offense.
Hope that helps you out! I'd suggest you play cheiften, maybe a standard map, maybe only 4-5 opponents a few times to get your feet wet. There is a ton to do and choose a civ to your style. If you like to warmonger, play a militaristic civ like China. If you just want to grow culture, try Egypt (although Egypt can be pretty potent as a fighting force too).
Have fun!
