Currently we have a website based on Pmwiki, which needs to be expanded. The idea is to combine it with a CMS, something like Joomla. So we keep the data and wiki functionalities, while introducing user authentication system, discussion forum and other features.
The question is, where should I start looking into the problem? Is there any books or blogs about how to combine web frameworks? Any suggestion will be really helpful!
PmWiki is a CMS, so depending upon what you want/need to do, you could extend PmWiki to do all of those things.
It comes with user authentication, and there are extensions ("recipes") for forums, blogs and other features.
Have a look at the entries under Administration which include a lot of variations on authentication (and other tasks).
You should also look at CMS category.