Hi Polete --
Your opportunities are hit and miss here. As professional teacher who pays my 200€ a month for social security and am registered under the "regimen autónomo" (freelance/self employed), Iīd be remiss if I didnīt say that it infuriates me the lack of seriousness that is given this profession. Companies and schools, looking for the easy way out in hiring native speaking teachers know that there are a wealth of "illegal" native speakers here who are willing to teach. So, they simply hire them illegally. Meaning, no permanent contract is offered, but rather some sort of "agreement" between the two parties...and this agreement does not hold water in court should the academy or company decide to stop paying you. Unfortunately, that has happened all too frequently recently here in Spain with the closure of Opening English, Brighton English Schools and Oxford English leaving thousands of students and teachers in the lurch.
But this is a long response to what should be a simple answer for you. If you are "selling", they are buying. Meaning that many companies hire while turning their backs on your legal status. There are some places that do demand legal status and working papers, but others that just donīt care. All they want is a native speaker (first), teacher (second) to be able to throw a warm body into a corporate classroom.
Apart from the academies and consulting agencies, your other option is to post signs (cartelitos) with your name and number and offer freelance classes that way....directly to individuals. Or take an ad out in a newspaper such as Segundamano announcing your services.
I also recommend that you check out
Expatriate Cafe which is a website dedicated to teaching English in Spain. I am certain you will find the information there very helpful.
Good luck with your endeavors!