OK Guys ... just finished the game in 1615 (233 rounds) ...
First i have to say this is a great thread to learn how to play civ 5
this is what i attended to:
-have one city, but many puppet cities
-have a good starting position with: marble,1 other luxury or more, long river (build next to it!), some wheat(at least 2) many hills (production is really important, more than food, i'd say, because your city gets much food from maritim CS), horses would be fine too but its not that important because u probably get horses from CS, coast to explore other conts, and most important is to have other civilizations near by
----> i had: marble,1 other luxury (3 ivory) long river, 4 wheat in 3 hex radius, 6 hills (wasnt that much

), horses, NO coast (i explored other civs and CS with 3 scouts as soon as i got navigation and met all other civs and CS really fast, 1 civilization near by and 4 in range but on same continent
In the beginning i puppet Kyoto with 1 warrior and 1 speerman(got from hut) therefor i build a warrior instead of a scout and had my first puppet city within 14 rounds i think. The other civs settled far away so i decided to take a military CS next to my city with the same army

(to puppet a city state with 1 warrior and 1 spearman u need to have free promotions to ur spearman and/or warrior at the beginning of the war to recover them immediately. So i got 2 puppet cities in round about 30 turns. They gave me a good advantage to my research to fastly reseach acoustic for the additional food bonus from maritim CS. Of course u must be allied with him but that costs money. To get much money u should often trade with other civs. Try to trade everything u got: open borders, luxury(if u can release some), strategy resources... But its important to explore the world to met other civs and CS to get money and culture/food bonus. I built Chizzen Itza befor the 500-happiness-golden-age.
I took more puppet cities with a 3-horse-army and my empire grew.
The limitating factor for me to get a fast win was culture ... i built cristo many turns faster than starting the utopia project. So u should focus on culture not too late! The main city and cultural CS (20 culture points per CS at the end) are the main culture producer. 1 Puppet city produced at the end of the game 9 Culture points per turn ... so u should get many puppet cities if they should produce many CP too but than ur happiness drops down ... balance it
My policy way was: 2 tradition 5 patronage and 2 freedom ---> save up ... but i think of getting the culture bonus from Piety and take happiness policy from patronage too and then save up ... dont know if this helps
I bought the most buildings and concentrated on getting wonders!
At the end i noticed that i had no coal in my empire but i solved this problem by puppet a maritim allied CS with coal in the borders
---> have a high research at the beginning and many culture points per turn later and be able to change over to a huge production to get those key wonders and utopia!
yeah .... i hope i can help u with this review ... if u have questions just ask here
peace up