Many books mention that for SW quality approach (including testing), one should adhere to and depend on the quality system in the organization. I assume that is QMS based on ISO 9000 which I have no experience with. As far as I know, this standard is a generic one and not specific to software. Would anyone advise as to how this is implemented?
I do not recommend relying on ISO-9000 for guidance on software quality.
ISO-9000 describes a heavy-weight procedure for how companies document all their processes. That is all; it does not address how to create quality. ISO-9000 makes a lot of sense for manufacturing. If you run a factory, and your employees do not have a shared understanding of how things are done, it is possible that misunderstandings will lead to defects if your products.
Of course, even in a software company, there is value in having a shared understanding of how things are done, e.g. coding standards, design principles, bug tracking, progress tracking, customer support processes, contract writing, and so on. You will have to decide whether your biggest quality problem is the lack of rigorously documented procedures. The answer will depend on what industry you service, what regulatory regimes you work under, and the risk tolerance of your customer base.