It's useful to have an apprentice, they give you a bonus when working in the lab. I assume you could also have them do scut work, like fixing arcane links or making Items of Quality. Stuff that takes a season but has no lab total. How does that work? Do they need their own lab, or can they work in yours while you are doing something else?
I let apprentices use communal labs too where they are available. I tend to get apprentices doing all the grimy stuff that takes up odd hours here and there for the covenant. Things you nede to be a magical person to do but dont take a huge amount of time or especially a huge amount of skill. Such as when gathering Vis sources. You get an aprentice to do that, maybe even get him to transfer it into a useful form.
I would not let an apprentice use the same lab as the owner in a season where the owner is performing a lab activity though.
Ever work in a small kitchen with someone else making a different meal? Ever let someone work in your garage and then try to find tools that they put away "right where they found them"? Multiply that by dangerous substances and botches and Twilight, and then again by Arcane Arts and quirky magi, and you might have some idea of the result.
So I'd say "no" - one lab, one project, one lab total.
I'm not even convinced that different magi can "share" a lab from one season to the next - at least not one with any sort of serious bonuses. Every description of a lab implies a "personalization" that doesn't seem to fit with someone else doing their thing last season and you stepping in and getting a full benefit, and then you leaving it perfectly prepared for yet a third mage the next season.
A basic +0 lab, maybe, sure - but anything more starts to get suspect imo.
I've always felt it would make sense for a covanant to have at least one basic lab specilized for instruction that is used and mantained communaly. It couldn't have any refinment bonuses (refinment 0) but it shouldn't have any penalties either. The covonant could add various feature that make it better for teaching allowing mages to teach each other spells without stepping into each others lab. Other dedicated labs could be developed as needed, a portable lab and/or a lab specilized in vis extraction for high auras come to mind imediatly. Building and mantaining labs could be yet another use for seasons of service.
Your apprentice would be very familiar with the set up of your lab....
But I still wouldn't allow two people to work the same lab in the same season...
If the acticity requires no specific lab total, who cares how suckingly bad the lab is? Just spend the one season setting up a -3 General Quality lab for investing vis in devices, fixing arcane connections and so on.
I agree that only one person can work on his project per season per lab. Sure, that person can have multiple assistants, but only one project is worked on. If you want your apprentice to do some simple stuff, either set up a secondary lab or let him have yours - you can just read in the meantime.
It might be useful to have a neutral lab to use when one magus teaches another. But my Jerbiton has a lab with Activity Spaciality in Teaching, so he'd want to use his own.
If you have the time and space, you might want a "neutral lab" highly specialized in Creo Vim Vis Extraction.
I wasn't worried about how bad the lab was. I was thinking that I wouldn't want my Apprentice to spend a lot of time out of my sanctum. There is the Code, but things happen. So, followup. What would the writeup for having an Apprentice lab attached to my lab look like as a lab virtue?
+1 space, -1 safety?
Xavi
There are rules in Covenants about using labs once they've been refined. Generally they fit what Cuchulainshoud suggested. I believe you need to spend a season to tailor the lab to yourself, and if your Magic Theory isn't high enough you may lose some virtues.
Chris
I think the past posters have done little lab work with apprentices. Based on the experience of family and friends (I am the non-scientist in the bunch), it is very common for graduate students and even post doctorate candidates to work in a primary investigator's lab. I see these relationships very much like a magus-apprentice relationship. In fact, the apprentice bonus should reflect the fact that they can sit and watch the time points, stoke the fire, etc. while the magus is busy on other aspects of his lab work. Certain lab duties such as transferring Vis and fixing arcane connections should be mindless activities suited for an apprentice. I also don’t’ think that an apprentice would necessarily get in the way, you are telling them what to do, it is part of their education, and if they are annoying you, then you banish them or make them sit in the corner. (Works for the post-docs).
Furthermore, I don’t think having an apprentice in the lab changes the rules for personalization. The magus is personalizing the apprentice in their education and training. The Code’s description of an apprentice as being considered part of the magus’ magic reflects my position that apprentices for purposes of lab work should be considered appendages of the magus. They bonus they offer is their intelligence, magic theory, and any applicable virtues and flaws. I can easily see the perfect Bonisagus apprentice being kept in the lab beyond the time they should have completed their apprenticeship due to the value as a lab assistant.
If you have a crappy apprentice your magus suffers the penalties. Maybe require lab roles when apprentices are involved since everything they do for their master would be stressful.
It's outside of the expected, but since all the equipment and materials are duplicated, you'd treat it as a second lab for all purposes (cost, upkeep, its own virtues, etc), but the mage would include it under the aegis (small "a") of his Sanctum. (Even if they "shared" some of the rarely used basics, you're talking about doubling the standard amount needed, and so doubling the basic cost to equal a second lab.)
In Covenants (sidebar, p 109), it talks about "2nd labs", and has some restrictions, such as a lab not being able to be on two different floors (even if connected by a stair), and that a "Sanctum" can only cover nearby workspace. However, since two different "magi" would use this, it could be on two different floors, or even in nearby buildings (again, within limits of claiming a single legal "Sanctum"). Or, if part of the same larger lab (with another 500 sq ft dedicated to it, etc etc), the two simply don't go near each other's space.
A generous SG might allow some portion of an Outfitting or other virtue, and perhaps the upkeep for the basic space (for an overly large lab, for instance) would already cover that aspect - even remove an "empty" flaw - but that would have to be on a case-by-case basis, and often be creative in what parts of a virtue or flaw are covered.
This is how I would run it - but probabl insist that the 2 labs are physically seperate wether by walls of by being on different floors.
I don't think the issue is about us not understanding how research assistant work within the same lab as their professors, for example. I've been there. I understand it. I think it's a question of three things. First, it's about game balance. Second, it's about a mystical relationship. Third, it's about the term "lab."
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Game balance gets all messed up if a whole bunch of magi can together build one great lab and all work in it, sharing its bonuses, at the same time.
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There are bonuses for the shape of a lab. There are penalties for having too much space. In a real lab it's OK to have unused space; you can use it later if you need it. More likely you're worried about being moved to a new location because you don't need the space you've been allotted. However, in Ars Magica the project is tied to the entire lab around it much more so than similar things in the real world. Similarly, the project is tied to the whole season; you can't just switch off between different projects like you commonly can in the real world.
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You could have multiple labs in the same building that represent spaces for apprentices as well as the main space for the master. Others have mentioned this idea. Maybe some magic items could even be moved from one lab to another to transfer the bonuses around. Meanwhile this would all be considered one professor's lab with different projects going on. Now we're dealing with semantics.
Chris
Remember that a real science laboratory is not a Hermetic laboratory.
The presence of an apprentice (or anyone else) working on a different project could very easily upset some sort of magical harmony that is required for the laboratory to work properly. It's the Hermetic equivalent of bad feng shui to have the apprentice there.
Also, there is no suggestion in RAW that transferring vis and fixing Arcane Connections are mindless activities. Fixing Arcane Connections requires a laboratory, a season of work, and vis. Certainly it is something that an apprentice can usefully do, but it still occupies a whole laboratory. Yes, there are no complicated game mechanics that the players need to know about for Fixing Arcane Connections. However, it seems to be a quite complicated job in character.
I agree with Richard here, the astrological requirements for hermetic activity seem to be written such that only small interruptions to laboratory activity are possible. You are not, for example, permited to do a half season activity outside the lab and still do something easy inside it.
Presumably you needto do things on specific days in a specific order and this cannot be easily possible if two people share the same set of equipment in the same cycle.
I also agree that anything which takes a whole season cannot be written off as trivial. Even if no particular skill is required beyond basic magical training and affiliation to the magical realm, that does not mean logistically it is simple or that the requirements are simple.
The science behind a rocket motor is quite simple - it doesn't mean knocking one up in your shed is quite so straightforward.
Oh, so now you're a rocket scientist! 
A Hermetic laboratory is less like a scientist's lab and more like a mad scientist's lab - it's dramatic, it's fictionalized, it's quirky and exaggerated, it's temperamental and unpredictable - in short, it makes a good story.
I really like this.
Chris