All you really need to view satellites are your eyes. However, to make your viewing experience more enjoyable and productive, the following items can be useful:
Without a pair of binoculars, you can only see the brightest of satellites, especially if you live in or near a city. When purchasing binoculars, you should look for a pair with a relatively wide field of view and good light-gathering capabilities. A pair of 7x35 is generally good enough. Most astronomy magazines and websites advertise binoculars and give tips on what expensive stuff to buy.
Accurate timekeeping is critical in viewing satellites. You can miss a pass if your watch is off by a few seconds. A good digital watch or mobile phone is generally sufficient, preferably with a light number on a dark background. Still, a watch by itself is only part of the story. You must also be able to set the time correctly. If you have a smartwatch or use the clock on your mobile phone, make sure it is set to automatically update from the network. This way, you get a convenient degree of accuracy. Precision-minded people can also get accurate time updates over the internet using the network time protocol (NTP) and various sites and apps that connect to highly accurate atomic watches. But unless you do astrophotography and want to catch the exact time of an ISS pass in front of the Moon, your watch or phone is supposed to be good enough.
When watching for satellites, you will find yourself looking up a lot. When standing up and trying to look straight overhead, it is challenging to hold your binoculars steady and keep that position for very long. Investing in a good lounge chair can help your neck and back and the armrests allow you to support your arms and steady the binoculars while looking. And do not forget the tea bottle holder. Nights can get chilly.
A light source is recommended to find your way in the dark. But how do light and "night vision" go together? Well, red light is supposed to preserve night vision, so a source of red light is better than a white flashlight.
If you are unfamiliar with the stars and constellations, a planisphere or star chart can help you orient yourself to the sky. However, maybe what you need is already in your pocket? Some apps can do everything from providing charts to augmented reality, helping you locate celestial objects by simply pointing your phone towards the sky. Warm clothing is essential if you are viewing from a cold climate. A warm drink makes it more pleasant. Also, depending on your climate, you may need bug repellent to keep from feeding the mosquitoes and other biting insects.