It was probably through the wrist. When the Romans crucified a victim, the nails were driven through the wrists between the radial and ulna bones and not through the palms. The nail would have ripped through the palm because the palm could not withstand all the weight of the body but remember that the main issue is that Christ was crucified for our sins.

Luke 24:39-40

39 Look at my hands and my feet. It is I myself! Touch me and see; a ghost does not have flesh and bones, as you see I have." 

40 When he had said this, he showed them his hands and feet.
NIV

One of the possible reasons He is depicted with the nail in His hands is because most people don't think of the wrist area as part of the hand. The sheer weight of His body would seem to indicate the wrist area, which is the base of the hand.