As you outlined,
teaching in Prague is not the easiest country to find teaching jobs in.
My best advice would to enrol in a classroom based TEFL course in Prague. Something along the lines of a few weeks. Usually the school will then assist you with finding jobs locallly in Prague upon completion. When choosing the course provider, ensure it has this career support.
Before deciding on the course, ask them as many questions about the chances of lining up a teaching job, what the success rate is, and do they have a list of schools to recommend.
ITC-Training in Prague is a good place to start at. They have been around for a while, and have a good reputation.
All the best!