Thought Process for when to create settlers?

[Mr. Shadows]

My favorite opening is scout-slinger×3 then either a builder or an archer. My tech order is AH->Archery. My first settler gets finished around the time my initial army (4-6 archers 1-2 warriors) is done taking their first city. This guarantees you room to expand, delivers several cities and ensures that you have the muscle to deal with the barbs as they pop up.

 

[Arent11]

I've been playing regularly everyday since the game came out but I still haven't quite figured out optimal timing for creating settlers / expanding.

I've been leaning towards starting the creation of the first settler at 4 population and after I've completed at least one district in my first city and then after that I just try to fast expand to all nearby luxuries / strategic resources that are within 5-6 tiles from that first city as population allows.

Just curious if this is a good way to go about it or if I'm really hurting my early game by expanding so too quickly.

EDIT: On Deity

Is no one here looking at the tile yields? There are always 1-2 high yield tiles around (Sometimes even 4 food/2 production). I usually wait until the city has grown so much that it starts working the "low yield" tiles. Then I build a settler, since taking away a population unit in that case doesn't reduce the productivity of the city much.
In the meantime you can build war carts/other units.

 

[Wr4ith]

Is no one here looking at the tile yields? There are always 1-2 high yield tiles around (Sometimes even 4 food/2 production). I usually wait until the city has grown so much that it starts working the "low yield" tiles. Then I build a settler, since taking away a population unit in that case doesn't reduce the productivity of the city much.
In the meantime you can build war carts/other units.

Thats true, the ideal moment for buliding settler is when you are working your all very rich hexes (4 yeld). also think about early empire inspiration bonus, you need 6 pop. It is easier to get this with 2 cities. But if your starting terrain is very rich and you can take this 6 pop only in capital (pretty hard without harvesting food resources), it is very efficent to wait with expanding untill unlocking colonization. So generally you want to expand before colonization if your starting terrain isnt very rich and there are better and more valuable tiles nearby. There is also very important factor, housing cap. If your city grow with housing penality, you are losing food. So the best cities to pop settler are those who reached the cap. In this situation next city is effective transition of population, which can grow because of free housing from terrain (river, harbor) that coudnt grow in previous city. It is one exception, though. Since harvesting food resources isnt crippled by food penalities, you can use it effectively to grow cities already reached housing cap. In this scenario, it isnt efficent to pump settlers from those cities.

 

[MaximusPlatypus]

I have little to add that hasn't already been discussed, but a good time to pump out a settler is when your city is food-blocked (example: 4/5 housing, or 5/5 etc).
Also if you have 2nd/3rd cities as "baby factories" sometimes it's better to spend the few early turns getting granaries, and unleashing a bunch of settlers in a "rush".