Many Auxiliares in Madrid teach private language classes to insulate their paycheck and earn travel funds. People generally charge between 10-20€ per hour but you should look around on the Auxiliares private classes pages to make sure you are asking a fair rate.
Some good places to find private students and people interested in conversation exchange are Tus Clases Particulares and funnily enough, Couchsurfing.com, which has a big network of groups for interests in addition to language learning such as football and rock-climbin.
Another program is called Mingles, and they host language exchanges in bars. I know some people who have worked for them although not long term. They hire people to lead the discussions and though you do get free beers, your hourly rate isn’t all that high. A euro is a euro and a beer is a beer though!
This page about learning a foreign language is interesting.
Find Spanish intercambios anywhere in the world click here
After graduating from The University of Oregon in 2013, I found out about a program called Auxiliares de Conversación in people can come to Spain to work as assistants to teachers in classrooms. The program is through the Spanish Ministry and open to native English speakers who have at least a Bachelors degree. Technically one doesn’t need to have any experience speaking Spanish, as the job requires that you speak strictly English with the students to immerse them, however, I would highly recommend that anyone applying for the Auxiliares program have at least a base level of communication skills. Spanish speaking comes in handy at times such as the program orientation, working your way through the visa process and foreigners office, opening a bank account, renting an apartment, setting up your Spanish phone, communicating with your coworkers and boss, and the list goes on. For anyone interested in the program, I recommend doing research online as there are many helpful blogs and posts about the process, such as the Young Adventuress, a wonderful blog written by an expat with loads of info on the program as well as on regions, payment, hours, etc.
There is also an infinitely helpful Auxiliares group on Facebook that I referred to throughout the year and really came in handy when maneuvering through Spanish bureaucracy and whenever Murphy´s Law played out. I cannot emphasize enough how life-saving this online community ended up being.