Curious what it's like to be a teacher in Thailand? I can share my experience and hope it gives you some insight. I became a teacher only after I moved here, not before. I completed a 4-week long intensive TEFL course in Chiang Mai, then went straight into some temporary teaching jobs to boost my resume before landing a long-term tutoring job.
If you want to teach English, you're very likely going to need a TEFL certificate. I'm saying likely, because I know people who have landed a job without one. As a native English speaker, your skills are highly desired and respected here in Thailand, and it will be easy to land a job. It might not be exactly what you want or the highest paid, but they're there. However, I don't recommend trying to be a serious teacher without a TEFL or other teaching certificate. Besides having the real-life big-girl qualification of a degree, it helped immensely to prepare me in the classroom.
TEFL stands for Teaching English as a Foreign Language, and it's a certification that requires at least 100 hours of training and 6 hours of observed practice teaching. Most standard courses are 120 hours, but courses can be 4-week intense study or drawn out to 3 months. There are many, many different courses offered all around the world for a TEFL certificate, and they are constantly running and available. Do good research before you choose a school and make sure it's a reputable business. The price around the world shouldn't differ much and runs more or less around $1000 USD - if you see an extremely low price, it's a red flag.
A TEFL course includes a good basis in English grammar, how to manage a classroom, how to effectively communicate using TPR (total physical response; read: body language), how to plan your lessons and class structure. It touches on how to handle behavioral problems, cultural differences, and mine even threw in an extra class on the local language. It was better than I expected and fully prepared me for the classroom.
TESOL is another certificate option, but tends to be more geared towards teaching people who will be settling in an English speaking country, rather than teaching outside of your English speaking country. The TEFL and the TESOL have very few big differences and both are a good certificate option for teaching.
The Cambridge CELTA is your best choice for a top teaching certificate. It has the best recognition, and is a slightly more intense study, but is absolutely worth it if you are thinking of becoming a long-term teacher and want a strong base as an ESL teacher.