When you want to observe the night sky without using a telescope, you should first of all choose a night that is completely cloudless. Also, remember that the moon should be either absent or in its smallest size. The reason being the brightness from the moon‘s surface will hide some of the dimmest and the smallest stars.
Be prepared to spend the entire night. Therefore, according to the climate, you should be appropriately dressed up with few extra pairs of clothing nearby, so that you can put them on once the time passes by and the night becomes colder. You should have some items of comfort available too. These include a reclining or lawn chair in which you can easily look up without straining your neck.
After you have made yourself comfortable, now choose a place from where you can begin your observation. It should preferably a place which is as dark as possible. Therefore, you should position yourself away from any sorts of street lights, city light or lights coming from the apartments or buildings. These lights will obstruct the view of dimmer and smaller stars.
Initially, it is really very difficult to adjust your eyes to the night sky. The pupils of your eye would almost take about 30 minutes to adjust to the darkness outside. You may get disappointed in the beginning few attempts as you may miss some of the amazing things present in the night sky. But regular practice will make you an expert and you will discover lot new each time you look and observe the night sky.