Pierced his side - Which side is not mentioned, nor can it be certainly known. The common opinion is that it was the left side. Car. Frid. Gruner (Commentatio Antiquaria Medica de Jesu Christi Morte, 30-36) has attempted to show that it must have been the left side. See Wiseman's Lectures, pp. 161, 162, and Kuinoel on John 19:34, where the arguments of Gruner are fully stated. It is clear that the spear pierced to the region of the heart.
The link really says it all. John 19:34 only said that his side was pierced. Beyond that, there is speculation (and a source commentray making the point) but nothing can be ascertained for certain.