A good start would be the ISTQB foundation level syllabus. While the ISTQB seem to be a litte outdated in terms of their views on the software development process: A focus on sequential waterfall-like models - it is a good resource to learn the vocabulary of software testing. Furthermore it explains different types and stages of software testing: http://www.istqb.org/downloads/viewdownload/16/15.html
Yes, this is a real problem! I learned testing in a waterfall environment (basically followed IEEE standards, ISQTB processes) and now work at a company that is more Agile. So many of the skills/techniques are fundamentally incompatible.
