The Civilization Play by Email League held a tournament during 2010 (The Linda Carpender Memorial Tournament) with special rules (advanced start, small pangaea map, 2 humans, 2 AIs). I was lucky enough to win the 7 games I played giving me a perfect 7-0 record. The setup was pretty standard and the majority of my games boiled down to a very standard approach. When reporting the results of my 7th game, I mentioned that I would be reporting about this approach. Here is that report.
My approach to the advanced start was that I put down as many cities as I could (up to a max of 5). Each city got 1 or 2 workers, and if I had money left over, I would add population, culture for the border pop or build roads on forested hills. The general aim was to have enough workers to get my cities up to speed as soon as possible. I rarely purchased improvements and only fishing nets if I did. I never, ever purchased tech. My basic game plan was that the game would be over quickly, no need to invest for the future - get my cities up and running quickly and then build offensive units to kill the other human.
The idea when putting down cities is to try and push your boundries. Your city will reveal more tiles and enable you to possiblity put down more cities, further afield.
Here I am putting down my second city and luckily grabbing copper and horses (remember, this is a classic era, balanced resources advanced start, so some critical resources should be visible on the map).
In the end, I put down 5 cities, populated 4 of them with 2 workers and 1 with a worker and a scout (must try and find my opponent). As you can see from the screenshot below, the starting position isn't that strong ... not many rivers, and a real dirth of forests. I've started each city on protection (archer) while it grows (I did miss out giving my Northern city a fishing net so I had to swap the archer build to a fishing boat). My starting tech is always mathematics - why chop forests for 13 hammers when you can chop them for 20.
And there we have it - advance start phase all done, time to start the game for real ...