The soul is something we don't know much about. As a matter of fact, almost nothing. Probably once we have better technology we will understand a little of it like Allah mentions:
And they ask you, [O Muhammad], about the soul. Say, "The soul is of the affair of my Lord. And mankind have not been given of knowledge except a little." [17:85]
First there is the soul, then the body. Once combined, the person is created. In regards to Adam PBUH, his soul was created after his body was created:
Indeed, the example of Jesus to Allah is like that of Adam. He created Him from dust; then He said to him, "Be," and he was.[3:59]
However, for normal people, the soul was created before the soul.
Arabic Source: http://www.saaid.net/Doat/almgamce/26.htm