I looked for the moon last night and couldn't find it. It should be a waxing crescent moon.

I found this:
The moon's location in the sky depends on the time of day and the phase of the moon:
Rising
The moon rises in the east and sets in the west every day. The time of day when the moon rises and sets changes throughout the month. For example, during a full moon, the moon rises around sunset and sets around 6 AM.
Phase
The moon's phase affects its rise and set times. For example, during a first quarter moon, the moon rises around noon and sets around midnight.
Direction
The moon's bright side points in the direction of the sun, which is usually east or west. The line that joins the horns of a crescent moon together points north or south.