Here are some basic tips:
In the beginning:
Expand expand expand! Never stop expanding. Populate to accumulate!
Also, rush buy as much as possible in the begining. And put workers on the most productive tiles. What I mean by that is if there's buffaloes and wheat in your radius, the workers will automatically go on corn, but in the beginning, shields give you more of an impact later on. Also, if you're playing Deity, put workers on forest if you know your population is growing too fast.
Midgame:
Infrastructure! You can still expand, but build up terrain and trade routes. It's best to be in democracy so you can be ahead in science. Periodically put your luxury rates up to 100% for about 5 turns and put it down to normal. Your population can double that way. And if your civ is good enough, you can do all of the above PLUS bribe all of your enemy(s)'s cities.
End game:
If you're civ is too advanced to switch to Funamentalism, then bribe your way through. Or else you can just switch to fundamentalism and conquer the world by force, but I find bribing works better. Always leave one pet city, best if on an island, and have a few veteran spies to occasionally poison their water suppy so they stay at size 1 and sabotage whatever they're trying to do.
Build a spaceship and launch as late as possible to build up population.
The ideal situation in King:
3 cities by 3000 BC
1.5 million people by 0 AD
15 million people by 1000 AD
Control the world by 1500 AD
200 million people 1700 AD (celebration!), and starting to research future techs.
Spaceship arrives in 2020 AD