Software testing is an entire profession including having its own graduate programs, but there are lots of resources to help you get started from books and online, just poke around.
There are books just about testing (TCS), books about integrating testing into a development methodology(Agile and Scrum include testing), and plenty of books on specific testing technologies (JUnit, Cucumber, ...). Most modern languages/toolkits include at least some support for basic software testing (unit or functional) such as Perl, Python, Ruby or have it readily available such as JUnit for Java, NUnit for C#. For testing web applications go look at Selenium, a great package of tools for web testing that includes browser plugins.
And *plug* I've had great experiences with the online resources including low-cost online classes available from the AST, at http://www.associationforsoftwaretesting.org/ The BBST courses are very informative and quite challenging. */plug*