Spanish, the official language of Ecuador, is spoken throughout the country, although for many indigenous people it is their second language. Various dialects of Quechua are spoken in the highlands, while in Amazonía several indigenous languages are spoken, including Kichwa, Shuar and Wao.
It's helpful to know a smattering of Spanish in order to get around; however, most Ecuadorians in the tourism industry speak English (and sometimes French or German as well). For the most part, visitors should not expect the general population of Ecuadorians to speak much English.
Ecuador is one of the best places to study Spanish in South America. Ecuadorian Spanish is clear and precise, and similar to Mexican and Central American Spanish, and rates are cheap. Quito and Cuenca are the best places to study, and both have a plethora of language schools. Expect to pay around $10 per hour for private lessons. Accommodations with local families can be arranged. There are also schools in Baños and Otavalo if you want smaller-town experience.