If you are looking for English Teaching work one option would be to contact all of the people who offer English teaching jobs year round.
For example, check the current offer on CIEE. Once you find an offer, you can do the following:
They will call you as classes come in and the people they usually count on cannot accept them. The more people you meet with the better your odds are of getting work, so just keep spreading the word that you are currently in Madrid and available for work.
Also you can place free ads both on-line and in the published versions of the following publications: In Madrid, Broadsheet, Segundamano, Aprende Mas, Teach in Spain, Madrid Insider's Notice board.
Also, you should look at all of the classified sections of the above publications, etc. for job offers as there are a limited amount of English language resources and you will easily be able to see who is hiring or looking for people at any given time and sign up or remind them of your availability as they post new offers.