How does the placenta form during pregnancy?

Hint: The placenta is an organ that develops in the female uterus exclusively during pregnancy. It looks like a pancake. A placenta is made-up of blood vessels. It provides the nutrients, water, oxygen, antibodies against diseases to the developing baby. It also acts as the waste removal system.
The placenta attaches to the wall of the uterus and connects to the baby via umbilical cord. It also contains the same genetic characteristics as the baby.
A baby has only one placenta, but the mother may have two placentas if she is pregnant with twins. If the twins are Fraternal twins, then each baby will have one placenta. In the case of identical twins one can have one or two placentas depending on when the fertilized egg splits. If the placenta forms before the splitting of the embryo, then one placenta will be connected to both the twins using their umbilical cord to the shared placenta. But if the embryo splits before the formation of the placenta, then a mother may have two placenta for the twins.

Complete answer:
Formation of placenta: In pregnancy placenta starts developing very early. The time is about 4 weeks.
When a sperm fertilizes an egg, within seven or eight days the earliest form of embryo forms. It is a mass of cells that are implanted to the wall of the uterus.
Some cells from this embryo mass split away and excavate themselves deeper into the uterine wall. These cells form the placenta, when the other cells of the embryo mass form the fingers, toes and other body parts.
Within the upcoming two months the placenta gets developed. Small capillaries of the placenta turn into the large vessels and provide more oxygen and nutrients to the baby. It will complete its Herculean development during the second trimester.

Note:
The placenta takes over from the structure known as corpus luteum during the \[10\] to \[12\] weeks of the pregnancy. It holds the baby for the rest of the pregnancy period and continues to grow larger as the baby grows.
In the first trimester the corpus luteum performs the placenta’s essential functions. It is a typical collection of cells. It produces the progesterone hormone as well as some estrogen hormone.