While there are numerous indigenous languages spoken in Ecuador (including Quichua – in the Sierra, and Shuar – in the Amazon), the only language you really need to be concerned about is Spanish.
Here in Cuenca you’ll find that virtually every taxi driver speaks some, if not fluent, English, because of living in New York City. Also, English is taught in schools and colleges, so many locals have a very basic understanding of some English words. That being said, it is worthwhile having a basic understanding of Spanish.
There are numerous free courses online, and some computer based courses that can give a basic understanding. Also, once here, there are a number of very good spanish schools. You can have a private tutor for just $4-5 per hour, or you can join a group class for a little less.