When you first start expanding, Colosseums offer +4 happiness. You get +2 unhappiness from the city itself, and +1 per pop, so from the get-go, you can only have 2 citizens per city while remaining happiness-neutral.
Once you unlock Meritocracy (+1 happiness per trade route, effectively +1 happiness per city), you can increase the pop cap to 3.
Then, with Freedom (+1 happiness per 2 specialists), you can further increase the pop cap by 1 and assign 1 specialist (it rounds up; 1 specialists gives the same happiness boost as 2; 3 the same as 4). Now you're at 4.
If you get the Forbidden Palace, you can increase it by another 1 pop. This will allow you to grow to pop 5.
Finally, with Planned Economy, you get an additional +1 happiness per city, allowing you to grow to pop 6.
You can do plenty of things with 6 pop. Run a bunch of specialists if you're chasing a tech win, otherwise the standard practice is trading posts.
What makes this powerful is that you can have an unlimited number of 6 pop cities. All the happiness modifiers scale, hence the name Infinite City Spam/Sprawl/Strategy.
Edit- Since you'll also have happiness resources, if you follow the outline above, you'll have excess happiness. What I usually do is grow 2-3 production cities past the cap with any excess happiness I have. These will work on important wonders and stuff.
Even if your cities take, say, 20 turns to produce infantry, if you have 20 cities producing nothing but, you'll get 1 per turn.