The law reader program is unfortunately all but defunct in modern practice. I know two persons who were admitted after the law reader program -- one who went to law school _after_ the program and one who simply did the program. The program is typically set to run for at least three years years of roughly 15 to 20 hours a week of student time. The economics of education in modern practice have essentially killed the law reader program, which used to be how virtually _all_ attorneys were educated way back in the Colonial era. The Virginia Board of Bar Examiners website has all the details on the program requirements and the extensive program rules, both for the student and the mentor.
The rub mostly comes from the mentor's side. As a practical matter, the mentor has to devote an economically crushing amount of time to the student's studies. Under the program rules last time I checked (late 2005), there could not be any family connection between mentor and student, nor any form of paid employment relationship. Since the mentor would not be permitted to bill a client for time spent working with a mentor (since it did not directly confer a benefit on that particular client), and the client cannot be billed for a student's work (which would by itself create an employment relationship between mentor and student), there are very few circumstances where the whole arrangement can survive the kind of time needed to complete the program.
Also, since the student cannot be employed by the mentor or the mentor's firm, the student has to have another job sufficiently remunerative to support himself or herself through the program.
The time when I saw it actually work was when an older attorney was in "of counsel" status with an established firm. He had essentially retired in place as a principal of the firm, and formally worked part time. He devoted the rest of his available time to mentoring his law reader. The older attorney had been in practice in Virginia for almost 60 years and _literally_ knew everyone who was everyone in the legal scene in a very wide geographic area in Central Virginia. I was an associate in the firm at the time and frequently talked to the law reader. He was really enjoying the time, was learning a great deal about how the law actually worked and was building up an impressive set of professional contacts through his relationship with his mentor.
If you can find the right relationship between mentor and student, this can be a hugely valuable educational experience. It can also fall apart for the most trivial of reasons, in which case the student has to start all over again.