Where and When to Look for Jobs:
Teaching jobs are mostly found in the three biggest cities, Quito, Guayaquil, and Cuenca. Quito is the capital of the country and the second highest capital in the world. It is a large metropolis with incredible architecture and a rich history with plenty of opportunities in for teaching. Cuenca and Guayaquil are smaller but are very popular destinations for English teachers. Outside of these cities you may have a hard time finding legitimate work and proper wages.
The primary hiring times are February - March and July - August. It is possible to find jobs online from your home country, especially if there are American companies. Also, you can easily use the internet if you want to take advantage of programs that offer certifications followed by placement. Otherwise in order to find work it is recommended to go to the city (with some savings to keep you afloat) and begin the journey of looking for work. This way interviews can be easier and makes hiring you much easier. Perhaps teach private lessons while you look for more steady work.
Although it can feel like you are in kindergarten relearning the alphabet as you navigate all the certification acronyms, TEFL, TESOL, TESL, EFL, ESL, and CELTA, they are not entirely all that different (although CELTA seems to be seen as the best of them all) the best English schools in Ecuador require one of these certifications as well as teaching experience. Many schools require the TEFL or teaching experience, and if you've got those, they may be willing to waive their normal undergraduate degree requirement. It's also possible to get a teaching job without TEFL training but if you are certified you will qualify for better schools and probably make more money. If you have an undergraduate degree in education with a US teaching certification your prospects will be even better. There are plenty of organizations that offer TEFL training on site and assistance with placement.
Salary & Cost of Living:
The cost of living in Ecuador is among the cheapest in South America. If you have any amount of savings when you arrive you will be able to sustain yourself for some time and or supplement your income fairly well.
The average cost of living is around $400 - $600 and you will make at least that much. At any school and more depending on your qualifications. Obviously your choice of lifestyle will greatly affect how for your income goes. If you are planning on hitting the town every night and traveling every weekend you may drain your account fairly quickly. But if you are content to become a true resident and live like the locals you will be just fine.
Jobs will rarely provide any type of housing for their teachers. In some cases at higher end schools and universities they may help you find housing but will not provide it. Use the local newspaper (if you speak Spanish well enough) to find housing. Also, connect with other expats, through groups like the South American Explorers (SAE) or Expat Facebook Groups. SAE requires a fairly small membership fee but provides a lot of assistance through their Quito clubhouse and may be able to help giving suggestions for housing. Likewise, you will be very hard pressed to find any programs that offer to help with airfare.
Classroom & Work Culture:
Women should know that as in many Latin American cultures it is a very patriarchal society and machismo is a real cultural characteristic. So, be aware of this in how you dress, especially in the classroom when teaching both adults and teens.
Students and teachers can develop relationships and friendships just like in the US. Especially when working for a family in private lessons you may come to seen as part of the family. With classes of adults you usually have students that are very willing and dedicated to learning the language. They will see the benefits and know the costs of being there, they will work hard for you and you won't have to worry too much about being assertive or a task master. When dealing with teens this can be a different issue.