I was lucky enough to be introduced to the system via an apprenticeship. And I do mean lucky, because it means you can acquire the vocabulary as well as the different rules little by little, while already getting to grips with the system. One of the things I find frustrating in a lot of role-playing games is not having the basic life codes (like standard questions about beliefs and behaviour) that my character, through his life experience, has.
Ars magica has a certain number of mechanics and vocabulary that an adult magi has inevitably learnt during his apprenticeship. (gauntlet, tribunal, quaesitor, twilight, pawn of vis, source of vis, base of knowledge about code, oath, etc.) And playing the apprenticeship, even in part, can be an excellent introduction.
At the moment, as a storyteller, I'm introducing three new players who have never (or hardly ever) touched the system. Considering the amount of time I'm playing with them, it's a maximum of 2h30/3h games. All the progression is done on a season-by-season basis, set by me for each of the characters so as to reflect both the character of their house (there's a Verditus, a Flambeau and a Tytalus) and that of their master. That give some more experience points that standard construction by book. I counted +/- 2 seasons of service (xp exposure only), 1 season with a book, and 1 season teaching. (instead of 3 exposure for 1 teaching)
This is how I managed the start of their game:
session 1: character creation in the form of a short questionnaire allowing them to define their character's origin. Does he come from a Jewish or Christian community; Catholic or Cathar; a city or country childhood? The childhood of a street urchin or a well-to-do family boy?
Then ideas of what they wanted to do as a type of magi in the long term, based on archetype, but also more generally the ideas they had. I then proposed a series of virtues/flaws that we adapted after explaining them.
Session 2 (1205 -opening of the arts-): I introduced them to their character, their story and their master. We started the story at the age of 8, with their opening of the arts. They built their first spell, with a big explanation of the magic system and its limits. They had a mini-adventure to go and collect a source not far from the covenant. There were no opponents, just the natural elements to deal with.
The source in question is at the top of a mountainside overlooking the covenant and you have to change a piece of cloth every season; except that their parents didn't know that there had been a landslide blocking the path.
Session 3 (1210 - 5 years after opening): Time jump.
The winter is particularly harsh and the magis are tense. Provisions have disappeared from the storehouse. The situation is particularly upsetting for the magis, especially as it was Christmas dinner that was eaten first. Young Tytalus's kinsman threatens her with a severe punishment, certain that one of the apprentices is responsible for the theft from the kitchen. The apprentices decide to investigate, with the discreet help of one of the other kinsmen.
This gives the apprentices a chance to experiment a little more with their magic, but also with notions of concentration, finesse and penetration, as well as might, then Aegis, rituals and arcane connections (depending on how they manage).
Session 4 (1214 - 9 years after opening): The year of the tribunal. Travel to the place of the tribunal. This session is primarily a presentation of the geo-politico-economic situation in Provence. A bit of dealing with socialites.
Sessions 5 and 6 (1214 - tribunal): Very heavily rp and political sessions, with little or no magic used (they haven't received any tokens). They have been given certain instructions by their parents, including to find penpals and to observe certain things.
These sessions enable them to familiarise themselves with the order as a whole. What is a Praeco, a Quaesitor, the oath, major crimes, what is a certamen, a wizard's war; how does the court work, how do the votes work... But also to introduce them to the major characters of the tribunal (primus, praeco, chief quaesitor, chief of the red cap, leader of the major covenants, certain other magis who may become recurrent later on), as well as to make the first contacts.
Session 7 (1217 - 12 years post openings): Time jump
First detailed laboratory work. How spell research works, how the level of the laboratory is calculated, how experimentation works... As well as an introduction to enchantments.
session 8 (1220 - 15 years post-openings): gauntlets.