If you want to find a place with Spanish university students, you should first come to Madrid and stay in a short term place from week to week.
Then walk around the campus writing down all of the room offers off of all of the bilboards you will see. There are many noticeboards so you will have to look at all of the easy to find ones outside and then go deeper into each 'facultad' for the ones next to the libraries, department head offices, and Erasmus / foreign student offices.
You can also check with the people at the foreign student offices if they know of anything. After this it would be the Segundamano Newspaper, but be sure to ask if your are speaking to a 'particular' or not as many agencies take advantage of this to hook you in.
Each landlord will have their own requirements, but paying one month's rent as a deposit and signing on to the end of December / February and the end of June is usual.
Prices for short-term room rentals in a shared flat in Madrid tend to be between 350 euros and 500 euros. The cheaper end of this scale is usually only available well outside of the centre or for low quality rooms.
Average prices (2008) from http://www.openingdoors.tk ()