I can't recommend anything specifically... practically any book that describes black box testing will tell you everything you need to know. You learn 99% of it on the job. The only prerequisites are basically word processing and internet skills.

Anyone who charges money for a product or service, produces a physical or software product, or supports different use cases will have some kind of QA. Often medium-to-large web companies have QA departments to make sure design changes don't blow up the site for different users. Different industries do QA differently (for example, medical device QA or anyone supporting ISO 900X is more rigidly structured and policy-driven than web dev QA).