I am very naive in philosophy. Is it right to say positivism is the belief that all truth can be known by verification by experience? If so doesn't Hume's criticism of induction already refute this? I hear that positivism has died out in the philosophic traditions. If so what has replaced it. Is Karl Popper's ideas about falsification a good replacement. How is all this related to scientism? And what constitutes scientific thinking in general and what does it say about epistemology?
Karl Popper's ideas are not primarily about falsification. Rather, Popper explained that all knowledge is created by guessing controlled by criticism. For a guide to reading material about Popper see:
Rational thinking in general involves taking seriously the idea that you are fallible and could be wrong about any idea you hold, and everybody else is in the same situation with no exceptions. There is no special group of people who should be considered immune to criticism. Science involves using a particular method of criticism in some cases: experiments and observations. Many ideas can be ruled out without doing experimental investigation because they are bad explanations, e.g. - creationism (see "The Beginning of Infinity" by David Deutsch chapter 4). When an idea survives such criticism and can be tested that's the sort of thing that good scientists are doing.
Scientism is where people pretend to do science without taking seriously the requirement for good explanations. This often involves claiming to do an experimental test of an idea that is a complete failure as an explanation. The worst instances of this commonly come from the "social sciences". For example, it is common to scan the brains of people with different behaviours and then say the brain activity causes their behaviour. This is about as sensible as claiming that patterns of ink on a page cause a book to contain words. In reality, thoughts explain patterns of brain activity, and the words the author chose explain the patterns of ink on a page, not the other way around.