You move your character by walking around in the real world. Your movement is detected with GPS, which requires your phone to have location detection enabled. It is usually found with this icon in your settings:
The game shows your heading in real life with the white cone that rotates around Moomintroll. If your direction is not right in the game you can try to recalibrate your phone compass by making a figure 8 with it.
You can measure the distance of how much you need to move in real life to reach a certain location by tapping outside your interaction range. Your interaction range is shown by the blue circle that is around Moomintroll.
Sources for GPS and calibration pictures: