The best way to visit the Mount of Olives is to take a taxi or bus (number 75 to Et-Tur, from the Damascus Gate bus station) to the top of the Mount, visit the points of interest there, and then walk down the hillside through the Garden of Gethsemane and the Jewish cemeteries to the Kidron Valley.
To get to the Mount of Olives, get to the top of the mount and walk down through the Garden of Gethsemane to the Kidron Valley.