They happen naturally. As populations become more and more developed and the child becomes a financial strain as opposed to an extra worker in the family work force, birth rate drops.

In most of Europe and Japan with absolutely zero effort population growth has gone negative.  As China has developed, its population growth has declined.  India remains undeveloped and it will soon pass China.

The U.S. is an interesting case.  Due to the large number of people living in poverty and therefore having an undeveloped mentality our population growth remains positive but if you look at the wealthy, or even middle class, you see very little natural growth.

In short, the answer to population growth is development.  Unfortunately the more developed a country is, the more resources it uses per capita so its a double edged sword.

I'm sure that completely allayed your fear.