The penis begins to grow when puberty starts. It becomes thicker and longer; the growth might not be too noticeable when the penis is flaccid but will be more pronounced during an erection. Also, the rate and maximum extent of growth may vary.
Along with the penis, testicles also enlarge during puberty. The testicles are a good marker to use to determine when the penis will start growing. When they start to increase their size, the penis will follow suit.
It stops growing when a boy hits the end of his puberty. Male puberty typically starts around 10 to 14 years of age. And usually ends around 18 years of age, but it can also stop at the early age of 13.
In most cases, males experience penis growth spurt around the ages 12 to 16. After puberty, the penis growth is considered impossible. And whatever size it stopped growing, then it will be deliberated as the maximum size according to inherited genes (read more about the average penis size here).
To achieve penis growth after puberty, you need to use various tools and perform special exercises. The most common methods are to use penis pumps (as people have reviewed here) or extenders like SizeGenetics. You should also perform jelqing – which is a specialized type of penile stretching.