The 'receiving' or host colony is the one at the bottom, this is the colony that still has it's queen and still has access to the outside (via it's normal entrance). The colony being united goes on top, separated by newspaper. It is trapped inside the hive by the news paper and has already had it's queen removed. It's foragers can not get out.
By the time the bees from the two colonies have eaten through the paper and combined you only have only the one colony and all foragers belong to that colony. They then all use the only hive entrance at the bottom of the original (bottom) brood box. Once this has happened you combine the two colonies back to a single brood box (or decide to keep them on double brood) depending on your intentions.
The paper slows down the combination to disorientate the colony being united and allow the united colony to take on the odour of the host colony, avoids fighting etc. This also means that when they do forage and then return to the hive they aare accepted because they have already been accepted into that hive, they won't 'fight' a second time (or shouldn't). It is usually enough time for the new foragers to emprint the new location, sometimes you can loose a few dye-hards to the old site though. A nuc at that location can catch them for re-uniting if the quantity is sufficient (sprinkle with icing sugar and bung'em back in the new hive!)
Hope that helps