What does an actual deputing require?
There are actually different “layers” of answers to that:
First, there must be a genuine necessity, including the fact that it’s not possible for the priest himself or another cleric to distribute, the person must be qualified, etc. etc. etc. I know you know all this, and for other readers, check the other threads.
The actual “deputing” part is a 2-part answer. On the one hand, the person should be appointed by some liturgical ceremony. The new Book of Blessings has at least one (maybe a few options?) for this–a very brief ceremony for appointing EMHCs to be used by a priest (unless they have been previously appointed as potential EMHCs by the bishop for a more stable period.) These prayers are “provided” but they’re not “required.” The Church prefers some kind of liturgical ceremony but does not strictly define what that must be.
To use the example we’ve already seen posted “hey, would you mind giving out Communion?” would actually suffice (in a minimalist sort of way), but it’s not the preferred way.
The other element of “deputing” is to remind us that when there is a priest present, the person can only become an EMHC if the priest actually appoints that person to help him in distributing Communion. To put it another way, there’s no such thing as an EMHC unless and until the priest makes the decision to depute one. Even in the case of those who have been appointed potential EMHCs by the bishop, it is still necessary that the priest decide within-the-Church’s-norms, that there is a genuine need, and that he “deputes” this person to be an EMHC at that moment.
Another way of looking at it is that “deputing” reminds us that the priest alone makes the decesion as to whether this is necessary and appropriate. To make it more concrete, I myself have been in situations where people “tell” me that they “are EMHCs” and that they “will” be distributing Communion at Mass. This is a teachable moment, and I use that moment to remind the person that unless I’ve appointed him to do so, he won’t be distributing Communion.