Double room in Madrid

I am Laura, 25 years old. I am living in England but moving to Madrid at the end of August. As I am travelling around Europe before I move, my aim is to find some where to live before I go on holiday.
 I would love to find some where to meet new people and learn the Spanish language.  I will be teaching in an international school.

If you know of anyone or any where then please let me know.