Whether you own a telescope, binoculars, or just use your eyes to observe the night sky, there are certain factors that must be taken into account to do so.

First, you need to know your way around, if you care anything about knowing what you're looking at. For this, sky charts (or maps) are very helpful in assisting you with orienting yourself beneath the stars.

Note, that located just outside the map are the four directions: north, south,
east, and west. Turn the map around so the edge marked with the
direction you are facing is down. The stars above the map's horizon now
match the stars in front of you, and the centre of the map is the
zenith (directly overhead). This particular map includes the names of the constellations, which is the best place to start when learning the night sky.

Another factor will be the Moon. If the Moon is full, you will be limited to what you will be able able to see because of the Moon's glare. These nights are best for viewing the brighter objects in the sky, such as star clusters, the brighter planets (Jupiter, Saturn or Mars), and of course, the Moon itself. You could spend an entire night just exploring the Moon's surface with a telescope, or binoculars, if you're inclined to do so. And of course the best time to do any night sky viewing would be during the period of New Moon. Which means there is no moonlight in the sky at all to hamper your observations. Some amateur astronomers will keep a Moon phase calendar handy (like the one below), just to make it easier to keep up with what phase the Moon is in.

One of the main factors that affects night sky observing is.... the weather. Clouds, rain, wind, or even fog can ruin a night out beneath the stars. More often than not, the weather will influence your observing sessions much more than the Moon,  or any other phenomenon. You will find yourself checking weather radar and satellite maps more often than worrying about what phase the Moon is in.

Depending on how you choose to view the night sky, on those clear nights, when the Moon is new, there are no clouds in the sky, or there is no fog to contend with; You can spend hours taking in the beauty of the constellations,  asterisms, star clusters, nebula, galaxies, planets, or any of the other thousands of targets that the night sky has to offer.