Hypothetico-deductive Method of Scientific Investigation

It involves identifying a toughest problem, of a given field, to solve. 

Steps

1. Guess a solution/theory that might solve the problem.
2. List out all the consequences/predictions of one's theory. This step must clarify what one will not accept as a solution, i.e, constraints on potential solutions due to your theory.
3. Compare the actual evidence ( astronomy, genetics, archeology, geology, climates, botanical, etc) with the consequences/predictions of a theory. Recognize that we can never prove anything but we can falsify. 
4. The process continues for the remaining observations/evidences. 

A theory that survive numerous such tests and that explains more observations than any other theory is considered a better theory.  Then comes the criticism (rational criticism is what is meant by criticism) and this leads to further testing of a theory.The theory also leads to new problems of higher complexity and one may start the same cycle, using same methodology, in solving those newer challenging problems. The process is iterative.