There are two main views held by Christians in regards to the origin of the soul. They are creationism and traducianism. Both of these views are held by fine Bible teachers.
Creationism- This view holds that God creates the human soul directly, out of nothing, and joins it to the body sometime between conception and birth (most would say at conception). In this view God is the primary cause and he does not use the secondary cause of human procreation in creating the soul. Thomas Aquinas and John Calvin held this view.
Traducianism- This view holds that the soul as well as the body is transmitted from parents to children through the procreation process. God is the primary cause of the creation of the soul but he uses the secondary cause of human procreation to bring it about. This view was held by Martin Luther and Jonathan Edwards.
In support of creationism Psalm 127:3 says, "Behold, children are a heritage from the LORD, the fruit of the womb a reward." Psalm 139:13 says, "you knitted me together in my mother's womb." And Isaiah 42:5 says, God gives breath and spirit to people.
I favor traducianism myself. Genesis 5:3 says Adam fathered a son in his own likeness and image. This probably includes the soul. Genesis 2:1-3 says God finished and rested from his creation work. This would seem to indicate that he would not create the human soul out of nothing. Finally there is the transmission of sin from Adam to all other humans (Romans 5:12-21). Traducianism explains this better than creationism. In creationism God would seem to directly create a human soul that is sinful. In traducianism the soul and body which are both sinful, are transmitted through human procreation. God often uses secondary causes to accomplish his purpose.