The Moon stays in the sky, in west and southwest (if you're on the northern hemisphere) a few hours after sunset when it's a crescent and a fre hours more when it's a half moon. When it keeps waxing and is gibbous (nearly full) moon it stays in the evening sky and night sky all night long. At full moon it raises at sunset and stays in the sky all night until sunrise, when the Moon sets in west. After full moon day (a white circle in calendars) the waning gibbous moon raises later every night but doesn't set in west yet before sun has already risen in east. The moon now stays in the daylit sky longer every day and sets always before the Sun in the west. Finally a thin C shaped crescent is visible only a few hours in east just before sunrise. It's not bright enough to be seen in the sky when sunlight makes sky bright forvthe day. With a telescope or binoculars you could still see it. If you start to follow how the Moon rises and sets every day, you will become familiar with it.