How exactly does the ICC enforce these decrees? Fly into Moscow and snatch Putin from his office? Fly into Texas and snatch George Bush from his art studio?

They would be arrested upon setting foot in a country that is part of the ICC. Similar to how interpol issues arrest warrants. However, since these are high ranking officials that will just not travel to these destinations it's a pointless exercise. It does however hinder these people from going on speaking tour after they have left office which many do.

How exactly this would play out if a country tries to arrest a head of state which travels with security is unclear. I highly doubt any leader or nation would attempt to travel to a country where there is that risk of such a confrontation.