The Moon takes approximately 27.3 days to complete one full orbit around the Earth. This is called a sidereal month.

However, if you're talking about the time it takes for the Moon to go through its phases (from new moon to full moon and back again), that's called a synodic month and it takes about 29.5 days.

The difference between the two is due to the fact that the Earth is also moving around the Sun, so the Moon has to travel a little further to catch up and be in the same position relative to the Sun.