How to find Teaching hours / jobs in Madrid

If you are looking for teaching work in Madrid you should contact all of the people who habitually offer teaching jobs year round like the academies / agencies listed at:
http://madridinsider.i8.com/work/placestoteach.html.

1). Call them to set up a face to face meeting with one of their representatives.

2). Email them your CV/Resume so they might have a copy handy for your meeting. (It does you no good to send them your CV/Resume before they are expecting it).

3). Meet with them in person to review your experience and availability.

4). Keep them up to date on your availability as it changes.
They will call you as classes come in and the people they usually count on can not 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 here in Madrid and available for work.
Also you can place free ads both on-line and in the published versions of the following publications, etc.
In Madrid www.in-madrid.com / Broadsheet www.spainalive.com / Segundamano www.segundamano.es / Aprende Mas www.aprendemas.com / Teach in Spain www.teachinspain.org.
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.