If you’re starting your search from home, there are plenty of web-based resources for finding jobs in Ecuador. The following websites are useful for listing current vacancies in the country:
If you’re struggling to find a job online, it might be worth going out to Ecuador to look for work on the ground. This is where Spanish language skills become almost essential. If you speak enough to get by, you can scout out opportunities, make contacts and find out from locals what the current situation is like regarding your line of work.
If you don’t speak any Spanish at all, then looking for work while in Ecuador is going to be a lot harder. If you’re dead set on moving, it’s highly recommended that you learn at least some basic Spanish before going out to hunt for jobs. By doing this, you'll be giving yourself a major advantage.