The rooms range from 700 CHF (shared apartments with shared bathrooms, often on lower floors) all the way up to a family apartment with two bedrooms on the top floor for 2,600 CHF.
You can find all of the different types of apartments available in the Maison des Etudiants on the Graduate Institute’s website.
While living in France can be much cheaper, depending on your nationality you may need to arrange for French visa, residence permits, etc.
and it may thus not be an option for non-EU or non-Swiss citizens.
That website also contains information on selection to the building, application, important dates, and more resources.
Most students live in one of the student ‘foyers’ (residences/dormitories).
The situation is complicated not only because Geneva is a rather expensive city (the 4th most expensive for expats in the world) but also because there is a serious shortage of rooms.