>OK, does that mean that I just dump her into the hive or do I make and use a push-in cage?
A candy cage will do if you have one left from some other time. Use marshmallows etc. or make a push in cage. The push in cage is the most reliable.
>I've never introduced a queen before and I know there are all kinds of perspectives on it, but I couldn't find "queen motel" on a search and wonder what exactly this means that I will be facing and how to introduce Her Majesty.
There are many questions and perhaps you can get answers before you get her home. If she's being caught from a nuc where she's laying she could probably be directly released since laying queens are almost always accepted by queenless hives. But a banked queen is another ballgame.
Brother Adam always direct released laying queens.
"the acceptance of a queen is not determined, as hitherto generally assumed, by 'colony odour'. but by her behaviour. A fully mature queen, one that has been laying for a considerable time, will have lost her original nervousness, and will behave sedately and calmly. When in that condition, her acceptance is assured irrespective of the safeguards generally considered as essential."--Brother Adam, Beekeeping at Buckfast Abbey
A package is also a special case as the bees are hiveless and have had some time to realize that there is only one queen and get used to her.