A few years ago I picked up a copy of "Yeast Culturing for the Homebrewer" by Rog Leistad (available here, among many other places:
It is a very good overview of how to approach this without spending a lot of money on lab equipment. I haven't actually done any culturing myself, but this book (booklet, really -- only 40 pages) gives me confidence that it can
be done, and on a tight budget.
The one issue not addressed in this book, however, is a mighty one in my opinion: yeast mutation. It really takes more than just a microscope to be able to watch out for yeasts that have begun passing on "flawed" gene patterns, and the fact is most hobbyists have neither the equipment nor the expertise to spot this (Homebrew being the exception). And mutation rates start to get mighty high after a while. I would hazard to say that few mutations would be readily visible under magnification to the uneducated eye, but instead, that they would become all-too-apparent in the fermenter -- exactly where we do NOT want them.
Maybe with periodic sampling by a fermentation lab this would become really viable, but I decided not to start up with this simply because I know that I don't have the skills or knowledge needed to maintain a pure strain of yeast for any length of time, and, that periodic testing by a lab would cost WAY more than simply buying fresh yeast for each batch. I really
don't have a lot of money to burn, but, at about $1 USD per 5g sachet, it doesn't seem like such a big investment. Of course, we are talking about our hobby here, so, from that standpoint, it isn't about the money at all.
Home yeast culturing is a fascinating adjunct to meadmaking, and I applaud -- and eagerly await the notes of -- anyone doing it, but it's not a branch of this hobby that I think I'll be getting into.