How can you act like prophet Obadiah?

The name Obadiah means "Servant of Yahweh" (literally -- "One who serves or worships Jehovah"). This prophecy has the distinction of being the shortest book in the OT. There are twelve different individuals in the OT with this name (a very common name), but no indication that any of these other individuals are to be identified with this particular prophet.

Nothing is known about his life, background or personality except what little can be inferred from this prophecy. It is assumed that he was a native of Judah. Others feel he may also have been among the circle of prophets attached to the Jerusalem Temple. The Jewish Talmud states Obadiah was not Jewish, but rather an Edomite proselyte God used to rebuke his own people.
So basiclly to be like Obadiah, is to be a servant of YWHW and be in continual worship and awe of Elohim.