Well, after reading the "books and scrolls" thread I decided to post this. Currently any dwarf can become legendary in any skill without any setbacks, every dwarf automatically knows how to perform the job they're assigned, though they might not be skilled in it. In real life, trade secrets like cheesemaking or smithing can die out in a town. I think dwarves with a skill level of "Not <profession" should be completely unable to do any jobs concerning the profession, and "Dabbling <profession>" dwarves should be grossly incompetent in any jobs concerning the profession, to point of being almost useless. Dabbling dwarves could often fail at whatever job they're doing, but still gain experience, though mayble less than they would gain from a successful job. For example, a farmer could fail when planting a seed and produce a stunted plant, and a weaponsmith could fail and produce a lopsided sword. Both would be literally unusable, the plant would be ripped out of the ground to make room for new crops and the sword would be classified as refuse. Essentially, dabbling dwarves know enough about the job to do it, but lack the experience to apply the knowledge.
(I'll refer to dwarves with a skill level of "Not <profession>" as "untrained" and dwarves with a skill level of "<profession>" as "trained" from this point on.)
As you can see untrained and dabbling dwarves are undesirable. However, dwarves could aquire knowledge concerning a certain trade from two sources: books, and other dwarves. With books, an untrained dwarf could be ordered to study a book concerning a profession and gradually gain experience from it until they become "dabbling." Poorly written books wouldn't be able to assist a dwarf past that point, but well written books could be used as a "field guide." A dabbling dwarf could carry a well written book with them while they work to refer to, decreasing failure rates and ultimately training them much faster than they would have been with a poorly written book.
An even better source of knowledge is other dwarves. You could assign untrained or dabbling dwarves a mentor and they would follow their mentor around while he/she works. The mentor would advise the apprentice and the apprentice would assist his/her mentor. The advantage of tutoring a dwarf as opposed to having him/her study is that as the mentor works, the apprentice gains full experience along with the mentor. This costs no additional resources and the apprentice doesn't affect the outcome of the mentor's job. Note that only trained dwarves can be mentors.
However a dwarf is trained, by book or mentor, the dwarf most work independently to gain more experience once they're trained, the book or mentor is no longer useful at that point. A dwarf trained in a skill could write a book concerning the skill, but not if they're dabbling in the skill. This could be done using the "Writer" skill. If you didn't guess it already, untrained and dabbling dwarves are restricted in the writing skill the same way they are in others, so they might have to read some books on writing or be apprenticed to a more experienced writer if they want to write a legible book. Books would be a valuable commodity as they could save your dwarves if the secret of a trade is completely lost to your fortress. Books in DF would be time consuming to write, and therefore expensive. Though simply buying books from a dwarven caravan would be the easiest, it would be expensive and once your writer(s) becomes skilled enough the books could become a good export. [I can't imagine human or elvish traders carrying any dwarven books with them, so you would have to get them from a dwarven caravan. Also, I haven't really thought about how the books would be made. See the "books and scrolls" thread.]
Dwarves don't have to be mentored to pick up knowledge from other dwarves though. Just casually talking with a trained dwarf would be enough to receive a very slow trickle of experience. While it wouldn't be much, it could be just enough to save you if your farmer decides to croak, one of the farmer's friends might have picked up some pointers on farming.
So how would this all affect the game? Well for one, it'd be important to make sure your dwarves have some level of experience in what you want them to do before you embark, and it could be worth it to bring some books with you. Immigrants would be more welcome than before as they'd bring previously inaccessible knowledge. As I said before, books would be nice to fall back on when your farmer dies and your populace is eating rats.