"If a soul is non-physical and the human body is physical, how does a soul stay in our bodies?"

I had a friend at college who was a big Star Trek fan (Bigger than I am. His room was decorated in Klingon.) He loved to ask the question, "What happens to the soul when someone is beamed down to a planet?" That is, if the body were dissolved into atoms, what would happen to the soul? There are a lot of questions about the soul's relationship to the body. 
Is the soul a part of the body or is it completely separate? Does the body die when the soul leaves or does the soul leave when the body dies? Does someone who is brain dead, but still on life support still have a soul? I was in the room when my wife's grandmother passed away and tried to see some evidence of the soul leaving, but couldn't. Some scientists even tried to measure the mass of a body before and after death to determine the physical mass of the soul. Unfortunately, the reason we know very little about the physical makeup of the soul because the soul is not physical. The soul is supernatural. It is the immortal part of ourselves. The soul doesn't die. The soul is what separates humans from animals.
We do know that the soul is corporeal. It has a shape and can be recognized. (Revelation 6:9) Apparently, our souls look like ourselves.(1 Samuel 28:14) And one day, our souls will be reunited with our bodies to either be rewarded in Heaven or punished in Hell.
How does the soul stay in the body? The Bible doesn't say. All we can say is because God allows it. When God decides to take it away, we die.