This refers primarily to how it's done naturally. That is, how does a person come into the virtues they have in their adult lives?
What is the process of Hermetic virtue transmission? Do Apprentices develop their own, do they only receive them from their masters? Does this take a season or is it some sort of process throughout the apprenticeship? What's the limit on this? If an apprentice already has a number of virtues from youth, are they limited to how many they can gain from their master?
I don't think there is an ordered answered to this (repeating - FAQ worthy?) question.
It seems clear that Hermetic traditions to transmit certain virtues & flaws from master to apprentice. I suggest to treat this as "initiation scripts" developed by the House or tradition, conferring V&F during apprenticeship. Each House generally has one, and individual traditions within each house may know more.
Generally, I think such "initiations" are spread over long periods, rather than focused in a single Season. The best example, I feel, is the depiction of the Tytalus apprenticeship in HoHS. This shows the gradual building of the tension over all of the apprenticeship until the apprentice snaps - hopefully in the right direction.
A few flaws, it is known, are caused by bad teaching - things like Deficient Art. Probably some others can arise in this way too, like Rigid Magic or so on.
Most mystical V&F, I feel, are intrinsic to the character and arise in him naturally as an individual expression of his Gift when it's developed in an Hermetic fashion. Thus, a person may have an Affinity with an Art, have Cyclic Magic, or so on.
If an apprentice has several virtues from youth, the master will typically need to "convert" them to Hermetic ones IIRC. For a PC, these Hermetic virtues will be limiting his maximum virtues, so limiting what the master can teach. An NPC need not be so limited.
I agree with all YR7's reply. As to what to actually do in game play, I take it you are trying to play through an apprenticeship?
I'd suggest that the troupe looks at the Virtues and Flaws that you want the apprentice to have by the end of apprenticeship, and compare this to what you think is sensible for him to have at the beginning of apprenticeship. Decide which ones it would be interesting to tell a story about gaining, and then tell some stories about the apprentice gaining these ones. Basically, treat every Virtue and Flaw you need to gain as a one-off Story Flaw. The story might be an initiation, a magical accident, whatever...anything that the troupe thinks is interesting.
For the virtues and flaws that you are not interested in telling stories about, I'd just hand wave them, and say "after 5 years the apprentice has gained these ones", "after 10 years, these ones", "by the end of apprenticeship, these ones".
Not just an apprentice, but a number of other folk, too.
I think I'd still take more or less the same approach. Decide what V & F the character should have by adulthood.
Decide which ones will make interesting stories, and tell stories about those --- or work the gaining of these V & F into other stories you were going to tell anyway. Handwave the ones that are boring.