How does a baby come about?

Do not get carried away and think that I am going to show you ways to make baby. For that, please go to Kamasutra on Cosmo.  

I can't compare it to the process of making babies, but I find the events that happen after the sperm-egg union pretty awesome too! It is an intricately orchestrated process of cell movement, replication and transformation. 

 
Sperm meets egg to form a zygote. 

The one-celled zygote then divides.

Early beginnings of life (Diagram from Univ of Maryland Geology Website)

In humans, around 5 days after fertilization, the embryo enters the blastocyst stage. It is now a hollow ball of cells. The inner cells constitute the inner cell mass (ICM), from which the embryo proper develops. The external cells (the trophectoderm) will eventually become the placenta. The embryo acquires a fluid-filled cavity called blastocoel.

Around the end of the fifth day, the embryo implants into the uterine wall. Extensive tissues form between the blastocyst and the uterine wall. Particularly, the syncytiotrophoblast cells actively invade the uterine wall to allow for nutrient exchange between mother and foetus.

The ICM develops into the late epiblast, a layer of cells that give rise to all cell types of the body. To make the different organs, the epiblast first undergoes a process called gastrulation. This forms the ectoderm (which becomes skin, brain etc), mesoderm (becomes heart, muscle etc), and endoderm (becomes liver, pancreas etc).