Visual Discovery in Dark Areas
If your scenario allows for people to venture into dark areas where stars are visible to the naked eye, then certainly that will be the easiest way for people to discover stars.
Non-Visible Light Astronomy
If your scenario requires people to stay in areas where stars are not visible to the naked eye, then techniques other than visible-light astronomy will need to be used. I'm not sure if all wavelengths in the electromagnetic spectrum have star detecting applications, but many do:
Gravitational fields are also means of detecting stars.
Problems of Developing Technology in Nomadic Cultures
Depending on how much time they are required to keep moving to avoid the noons and nights, they might not be able to develop enough technology to reach modern Earth's levels of technology. So many factors of modern technology have evolved in stationary workshops, where large, heavy, non-mobile things like a blacksmith's forge or a steel foundary's massive smelting apparatus can be built, maintained and operated.
Metalurgy and other technological fundamentals might be difficult to develop in a very actively nomadic culture. For example, if the days last for 9 years, but the planet is millions of miles wide, they may be required to move extremely rapidly all the time to stay safe from the noons and nights. If the planet is only the size of our moon, though, they could stay in one place for many earth years on end before having to move to a safer location, giving them time to build shops in which to develop non-mobile technologies (like Very Large Array telescopes.) If they do have enough time to build shops, but later have to move on, if they aim to, they can eventually come back to their shops when they have gone all the way around their planet. This would allow them to use stationary technology, just at a different pace and style from the way it developed on Earth.
So, the size of their planet will play a huge role in shaping their development of non-visible light astronomy technology.