The Department of Education and Skills provide annual funding to Education and Training Boards (ETBs) from which English Language tuition may be provided to adult migrants. Some English classes are free.
It is very important that you make every effort to learn and practice Spanish. Doing so will make living in Madrid a less stressful experience and will make it easier to meet local people. A higher standard of Spanish will also mean that you will be able to find employment and training possibilities easily.
If you don't speak Spanish, it's advisable to enrol in a course at a local language school, preferably before landing in Spain.
If you're planning to work in Spain it is recommended to obtain a formal qualification in Spanish for non-native speakers (Diplomas de Español Como Lengua Extranjera), administered by the Instituto Cervantes, as well as by other institutions.
This is one of the most important educational and cultural institutions. It offers Spanish courses abroad and it maintains a list of centres in Spain. Unfortunately, their web site is almost impossible to navigate if you do not already know Spanish.
Finding an exchange partner is the best way to practice a new language with a native speaker. Moreover, language exchange partners can help you understand the culture of the country and inform you of local events to attend. In the best case, an exchange partner will also turn to be your friend.
Many language schools, libraries or even bars, they offer conversation exchanges in Madrid, where you may be able to learn Spanish in exchange for conversing with someone in your own language.
Here, you can find some of the places where you can attend language exchange:
Exchange bars/pubs:
Groups:
Moreover, you can also find a tandem partner through EasyExpat's forums.