English jobs are available in Cuba but with the current state of the economy, preference for jobs is often given to Cubans. One way to overcome this is to be qualified and a native speaker; jobs then, can be found.
One possibility is going to Cuba with a volunteer organization who can arrange the job and placement. One possibly worth contacting is Grupo de Especialistas en Lenga Inglesa, which offers programs where ESL teachers can volunteer to travel to and stay in Cuba for periods of time to teach English at Cuban schools.
Meanwhile, the authorities have expressed the desire for Cuba to become bilingual (English & Spanish) so there is a demand for trained teachers. Experts predict that within a short period of time the country will begin to open up more and the chances are that when change comes in the near future there will be considerable interest English and developing interest in their US neighbors again.
Note that US Citizens can now travel freely to Cuba and work there. You will need to contact the State Department for details on how to do this.
TEFL pay is poor by Western standards with a maximum of about $200 USD (€158, £127) per month. This figure is high compared to local earners and it can be a lot less.
Schools vary. Some have computers and tape recorders but most in the state sector have much more limited resources. It’s hot and sticky in the afternoon (no air conditioning).
Regarding living there, be circumspect in your speech. And especially so if you have an agenda (promoting anything but the government line or spreading religion) as the chances are you’ll be found out and deported.