How it Works
The pop trick is the best way of increasing your population quickly, but it can be disastrous if done wrong. Basically, what you do is reduce the maximum population of each planet for one turn. The next turn you set the max population for all your systems back up. This will have enormously increased your ag ratio, so n the next update your population will have grown significantly, hopefully by enough to make a builder planet (50+ population.)
This is the one area in the game that I do use a calculator, just to make sure I get it right. Add up the ag of all your planets — this is your total ag value. Now divide that by your current population after you have reduced it for the trick (say 5 if you lowered one planet to 1, one planet to 2, and Home World to 2.) This quotient gives you your ag ratio. For each planet, multiply its reduced population by the ag ratio — the product will give the population on that planet next turn. Note: you can colonize during the same round as the trick, but make sure you count the these colonists in with the total population when calculating the ag ratio.
Depending on the map, it's quite possible that you won't have the ag to support all of your planets at their max population after the trick. Most likely, some planets will reach their maximum population, but some of the others will not. If you don't have enough ag, then those which do not reach maximum population will not grow. There are two ways of handling this. First, you can simply set all planets to max population, then trick, then build terraformers on low-ag planets so the other colonies can continue to grow. Second, you can purposefully set some planets to rise to populations below their maximum, thus saving ag and allowing the other planets to grow in the following rounds.
When to Use It
Note: when you reduce the population you reduce your production of fuel and minerals, so be SURE to dismantle your ships before attempting to trick (dismantle them on the same turn you reduce your planets' population.) If you do not dismantle it will cause your tech growth to plumet, perhaps even driving you to negative negative levels, at which point you cannot build anything. The only ships that should normally not be dismantled are colony ships set to colonize, terraformers set to terraform, engineers opening/closing gates (only if this action will consume the engineer) and ships that you know are going to be destroyed in combat. Only after you've mastered the trick should you begin experimenting in leaving ships intact, relying on your reduced resources and that from trade to keep your tech level from dropping too much. I sometimes do this to keep a science ship exploring; you just have to weigh for yourself whether this is worth the reduction of tech development it will cause.
Note that on an early trick you will probably set the populations of each planet fairly low, between 1-5 for each planet. Tricking is not limited to the early game, though. If you trick late in the game it is unnecessary to lower your populations all the way down. It may take some time to calculate the best combination of reduced planet populations, but you can usually maintain around 1/4 of your economic strength in a late trick, which means you will not have to dismantle all your ships while you trick.
There is also such thing as a mini-trick, where you gain fewer benefits than from a full trick, but which allows you to keep a higher economy throughout. There are actually several variations of this reduced trick. One way is to lower your Home World to 1/2 to 1/3 population instead of all the way down. This will result in a lower ag ratio, but since you have reduced your population by less it doesn't have to be as big to get Home World back to full strength. This type of trick will not bring a newly colonized planet up to full population, but it can give your population a significant bounce.
Another variation, though not actually a pop trick per se, is to simply lower the maximum population setting on several planets to 1 and let the other planets grow naturally. This will have the effect of increasing the ag ratio, which will increase population growth rates on the other planets. This is not a common practice, but can be used when you need a quick builder at the front but cannot afford to execute a full pop trick.
The actual ag ratio used in the game contains a "fudge factor" so that you must actually divide your (ag value + 0.1) by (reduced pop + 0.1) Thus if you have 150 ag and 3 planets all set to pop=1 then your total would be 150.1/3.1 = 48.4, rounded up for a final population of 49. Be sure to take this fudge factor into account when cutting your tricks close. (The need for this fudge factor has been eliminated at Iceburg so you can do your calculations without it there.)
While incredibly powerful, pop tricks are not without their dangers. If you try an early pop trick without having enough nearby planets explired, an enemy science ship can easily stumple onto your frontier planet and get an easy nuke. Later tricks must take into account cloakers that might be lurking about just waiting for you to pull a stunt like that.
Recognizing the importance of the pop trick, several servers implementing post-2.8 versions of SC have modified the game logic to change how pop tricks work. If you play in any of these games be sure you know the local rules.
Other Pop-Trick Resources: