You would be extremely lucky if you could rent a studio for under SFr. 1,000 a month in Geneva, beware! there's always an extra  communal charge per month SFr. 100 or so per month.

You will definitely need someone who lives there to assist you in finding somewhere to stay. It is not at all easy.

I lived there for almost 5 years, 5-min walk to Cornavin main train station, before moving to live in a house in Gex, France (not far from Ferney-Voltaire.

You may have to first stay at an apartment studio in Ferney-Voltaire France (10-min drive from Geneva airport), there are a few places in that town for you to choose from until you manage to find somewhere to stay in Geneva.    
http://ppantip.com/topic/35053077

https://www.tripadvisor.com/Hotels-g196701-Ferney_Voltaire_Ain_Rhone_Alpes-Hotels.html

They are not the cheapest, but what can you do without accommodation?

Bear in mind, the process of getting a place to stay in Geneva takes a long time. You may need to pay a professional to help you, that is if you can afford it.

https://www.google.com/search?q=regie+geneva+switzerland
http://www.thelocal.ch/20150312/top-tips-for-seeking-an-apartment-in-swiss-cities
https://www.justlanded.com/english/Switzerland/Housing-Rentals

Can you find someone in the organisation of your internship to share a place with?

Geneva Welcome Center (for international civil servants)
http://www.cagi.ch/en/housing.php

If you do need further help, feel free to contact me. If you are serious, I may be able to put you in touch with someone who lives there.

Good luck.