When you enter the door-knocking minigame, you're presented with a grayish bar with a red center. Furthermore, there's a white indicator that starts in the middle. When you hold your right joystick down (or move your mouse back), the white indicator starts swinging from end to end. By swinging the mouse or joysytick forward/up, you slam into the door. The closer your white indicator is to the center, the more damage you do to the door, indicated by the grey bar reducing. In order to knock down the door in one attempt, you must swing forward when the white indicator is in the dead center of the bar.
Note that, to make this easier, you don't have to swing forward on the first pass. As long as you keep your mouse where you moved it back or your joystick down, the indicator will keep swinging. Rushing it will usually only cause you to mess up.