Gears and bearings are one of the major components of many machines, which can result in operation downtime or even catastrophic failure of a whole system. This paper addresses a tutorial for the features extraction and selection of the gears and bearings, which is known as feature engineering, a prerequisite step for the prognostics and health management (PHM) of these components. While there have been many new developments in this field, no studies have addressed the tutorial aspects of features engineering to aid engineers in solving problems by their own effort, which is of practical importance for successful PHM. The paper aims at helping beginners learn the basic concepts, and implement the algorithms using the public datasets as well as those made by the authors. Matlab codes are provided for them to implement the process by their own hands.