Need more specific information about Time Machine

I'm finding it quite difficult to find detailed technical information about a Mac or what might be more accurate OSX. At the moment, I'm trying to learn about "how to use Time Machine (TM)". I've been able to findthis article which is probably good if you are undertaking precisely the use cases described. However, it does not really reveal how it works well enough to anticipate what might happen when there are slight variations in the use case. If Apple provides anything like an instructional manual for TM I'd be grateful for assistance in finding it.

With that said, my immediate undertaking is to deal with a situation where some outside parties who have now been determined to be untrustworthy have been involved in the installation of software and circumstances suggest that the subject Mac has been maliciously compromised. Therefore, the owner wants to restore the software to a known good state and then recover their work product from a backup made by running TM on the compromised system. This means that I have a TM volume from one Mac that I want to use on what I think is now a new (different) Mac for the purpose of restoring files. The new machine is not yet using TM and it looks like some setup is required. However, it appears to me that TM associates the backup volume with a specific computer which means I have no idea what is going to happen if I should specify the TM backup volume used on the old computer as a TM backup volume on the new computer. At this point, I don't really want any backup to be performed. I'm only interested in performing recovery of a subset of the files contained on the backup (i.e., old TM volume). If someone can provide specific instructions about how to do that it would be greatly appreciated.