In the very early game, pop-rushing is an important tool, especially if you're religious.
First, the facts: When pop-rushing, you need one citizen for every 20 shields you rush (so if you lack 21 shields you need two citizens), you cannot use more than half of your citizens (so a size 3 city can only pop-rush 1 citizen), and you get one unhappy citizen for every citizen that was pop-rushed. This unhappiness disappears after 20 turns.
Then, the use:
Many of your new-founded border cities (the cities that are far away from your capitol, and close to enemy cities) will only produce one shield per turn. After 10 turns, the city will grow to size 2 and have produced 10 shields, leaving 20 shields left to finish a temple.
This is the time you should definately pop-rush the temple. Your city goes back to size 1, but you get an instant temple. The temple will after a few turns give you a full city radius and those early temples mean a great culture lead early on.
The unhappiness from the pop-rush doesn't matter, because it will disappear after 20 turns when you're still size 2, and with a temple youre one unhappy citizen becomes content. On emperor and deity, you will have one more unhappy citizen, but this one is made content by one military unit.
So what you loose is one citizen and 10 turns of production for the gain of one temple, but both of your losses will soon be paid back by the fact that you get the extra 12 squares to work on .
Also, this is a great tactic if the enemy beats you to a resource by building a city adjacent to this resource. Build a city yourself adjacent to this resource, just outside the enemy's city radius, and as soon as you get the temple, your border will expand and give you the resource - and possibly culture flip the city to you some turns after that as an additional bonus.
Now, this becomes more difficult if you're not religious, since your temple need 40 shields before you can pop-rush it by using one citizen. This is actually one of the greatest benefits of religious, IMO. But you can still use this with non-religious civs, you only need to wait until you get size 4 and have produced 20 of the 60 shields needed.
Start using pop-rush this way, and you'll be able to see other opportunities, like sometimes rushing a courthouse in your size 8 city on flood plains, or pop-rushing the remaining part of your attack force before your first war.