The scientific method was a set of techniques used in various sciences in correcting, integrating and acquiring knowledge. The basic tenets of the method was to observe a phenomenon, theorize on the cause, and then attempt to prove the theory.
In 2369, while trapped in a game of Chula after a fraught first contact with the wadi, Bashir claimed to have solved a puzzle using the scientific method, but then immediatly admitted that he had in fact just guessed. (DS9: "Move Along Home")
In 2370, when Constable Odo impressed Doctor Mora Pol with his investigative skills, he commented that he was beginning to think that the scientific method and the police method had a lot in common and Odo agreed. (DS9: "The Alternate")