This animation shows how the phases of the Moon are formed. The left hand diagram shows that only one half of the Moon is lit up by the Sun. The large diagram of the Moon on the lower right shows how the moon would when it is at different places in its orbit when viewed from Earth.
The diagrams are not to scale.
You can see that a full Moon is always seen in the opposite part of the sky from the Sun. In other words if a full Moon and the Sun are visible at the same time one will be rising in the east and the other about to set in the west.