You apply for a TEFL job. The TEFL job requires you to have teaching experience. You can't get experience without getting the job. If there ever was a catch-22, this is it and it aptly describes the conundrum most TEFL graduates face as soon as they finish their course.
Most students resort to wasting their time with low paying job just to get teaching experience, so that they can qualify for better, high paying jobs. Even those who do land up good jobs straight off the bat struggle in their jobs because they just don't have requisite hands on experience to handle a big class. This is a very common situation students find themselves in as practical training is just not something that very many focus on. This is especially true for those who took their TEFL online and did not have the opportunity to interact with other students or indulge in practice lessons. However, there are ways you can get teaching experience before you step into a classroom and that too for free. These include
There are numerous NGO's who welcome volunteers and even people in your community neighbourhood who wish to learn English. You can thus help them learn the language while also improving your teaching skills. Just look up on refugee centers, churches, immigration offices, and community schools. What's more, it looks amazing on your resume as well.
Before you move onto big classrooms, you can hone your skills with some one to one classes. These help you improve your weak points and give you a "job" to put up in your resume. While private classes tend to be quite lucrative, you can offer free classes in the beginning to improve your credentials.
Alternatively, you can go online and try your luck teaching in the virtual world. There are huge number of opportunities available and many positions do not require prior experience either. You could do it from your home and teach a student from across the world. If you do build up a good reputation, you could earn some serious bucks as well. Some online tutoring companies you can check out are: tutor.com, italki.com, or tutorabc.com.
So yes, becoming a seasoned TEFL teacher might take a bit longer, but you can build your skill sets and your resume significantly with a variety of jobs, online or offline. Just take a plunge and see what suits you the most.