What happens when a child gets placed for adoption?

Exoplanet

It takes anywhere from no time at all (the day of birth) to years. The why, when, where, what age, and how is missing from your question. Most decent-sized public libraries have a law section with books on your state's adoption law. In the US there are no longer orphanages. This question has been answered many times.

Tri-Harder

The wait list for infant adoption is very long, and newborns rarely (if ever) go into the foster system. The only time that happens is when the parents' rights can't be terminated, such as a CPS case that's ongoing, or the mother is in prison with the father unknown, etc. Then the child primarily goes to family, with fostering being a second choice. Generally speaking, an adoptive family is chosen before birth, and the baby goes home from the hospital with them.

Ranchmom1

Infants typically go home from the hospital with their adoptive parents.

jane

they could potentially stay in the system until they are 18, at which point they get released and have to live on their own as an adult. They will live their entire life without a family and knowing no one wanted them

Anon

They could be in the foster care system for years. People who put their children up for adoption should not be allowed to have children again AND it should be a lot easier for children to be adopted.