The Moon orbits the Earth in a counter-clockwise direction as seen from the North side of the orbit. This is the same direction that the Earth rotates. The figure to the right shows the orbit and the phases of the Moon as related to the Moon's position in its orbit.
Because the Lunar phase, as seen from Earth, is determine by the Moon's position in its orbit relative to the direction to the Sun, an observer will see each phase at distinct places in the sky during the night. This figure illustrates the positions of an observer on the Earth for various times of the day. The Moon's location in the sky is related to the observer's horizon. The local horizon is a plane tangent to the surface of the Earth at the observer's location and if you project that plane into space you can deduce where the Moon will be with repect to the observer's horizon.
The above diagrams show 1st Quarter Moon at when the observer has rotated to be at sunset and at midnight. The horizon is drawn in each case tangent to the Earth at the observer's position. At sunset the 1st Quarter Moon is high in the sky while at mignight the Moon is setting.
With the above information you should be able to determine the location of the Moon in the sky given its Phase and the time of day. Can you? You can check youself using the menu below. Select the situation being considered and a diagram will show the correct position of the Moon.