If I remember correctly from watching the unveiling on television, the Eucharistic Host was placed into the glass container with the gold ring, (seen in this photo http://www.catholicnews.com/photos/08hp0217.htm) while it was on the altar. Then the container was inserted into the monstrance. I guess this way they can keep watchful eye on any particles that might fall.

I would imagine they would need a few priests on hand to consume the old Host when it needs replacing though!