For many, taking a vacation to Madrid is a privilege, one that allows for a week or two to discover the city and take in all the sights.
If you are looking into a more long-term stay, consider becoming an ESL teacher!
Madrid unemployment rates are at an all-time high, and a lot of Spaniards have started looking into learning English to heighten their skills and to make them more valuable in the workforce. (source: https://www.gooverseas.com/teach-abroad/spain/madrid)
Most of the programs require you to have a college degree and be a native English speaker. Having a TEFL (teaching English as a foreign language) certification is also normally a must. From there, there are several resources that you can look into that will assist with job placement.
Live amongst the locals, experience the culture firsthand, and become a resource to the citizens of Madrid. Being able to speak Spanish is not necessarily a requirement, but it will come in handy to further connect with your students and live your daily life.
If you begin working for a visa-sponsored program, you will make a flat monthly salary. What you make will typically be around 600-1,300 euros per/mo. The pay will vary depending on your work situation. If you need supplemental income, you can look into teaching private lessons, as well.
At the end of the day, the experience that you receive is going to be just as valuable and enriching as the skills that you will be teaching.