If you are a beginner and just learning about square pianos with the idea of restoring one, or more likely, you already have one and are looking for information to get started, there are a few questions you should ask yourself first:
Do I even have time to undertake such a task?
It will require approximately 250 to 400 hours to do a competent job on a poor condition square; and most squares are in relatively poor condition as-found. With at least 60+ hammers, each having 9 or more pieces to them, just to name one small part, a square piano is a very complicated mechanical beast. In addition, there is much to learn first before picking up the toolbox. If you have every Saturday available for the next year or so, then perhaps the answer is yes!
Do I have the necessary tools and workspace?
You will need all the usual woodworking tools, plus a number of specialty items like a wire brake, jigs and punches that you will make as specialty requirements dictate, and etc. Plus, you need to pick up some of the books on the subject to familiarize yourself with the subject, and ask a LOT of questions from those who are willing to help out.
Do I want to learn all this for just one instrument, or is this the start of a long term interest?
Frankly, it is a bit of a waste to acquire so much specialty knowledge only to use it and lose it. But if you are the type who wants to become involved in this interest, the long term benefits are rewarding, as the finished products speak in lovely tones.
Finally, “Am I a patient person or do I just want the thing finished and playing?”
Pianos are filled with repetition, not to pun too badly. Many activities will be done tens of times, same operation, next key up or down. If patience is your virtue, you have found a potential calling. If things usually lose interest after a few weeks then its time to call the professionals.
This site and many others list professionals willing to take on your task. As to cost, I will certainly not speak for anyone else, but imagine an average of 200 hours, and in US dollars something around $25/hour and you have at least an idea of where to begin to think about this. You can buy a restoration project for a few hundred dollars or pounds. A professional restoration will be far more expensive. Normal piano technicians are no better equipped than you are to help you most of the time, and the worst types are so certain of their direction and so wrong headed that the result will be a botched job. You must find the restorer with sensitivity to a period instrument. Perhaps they may quote a figure well below what I have referenced, but a set of strings from Malcolm Rose installed is around $500 and that is pretty well bare minimum.
So you at least have a financial incentive to learn how to do this yourself. I encourage the individuals who can answer yes to most of the questions above to have a go at it. It can be tremendously rewarding to bring back these ancient voices and hear them again, and only steady and careful work will do the job.