I mean, do I have to take a week-long course in order to teach ESL students? What is the whole process for TESL consisting of?

Be very careful about getting a certificate in TESL. As far as I know there are no regulations on TESL certificates. Many universities and schools offer certificates but choose carefully. Find a reputable school.

The CELTA or DELTA is a recognized program. I know of several people who have taken the courses. They are expensive, intensive and very helpful.

Check out www.eslcafe.com for information on Teacher Training.

You may even find that you do not need to get a certificate. In Korea, you need only a BA(any major) to teach EFL in schools or institutes.

A lot depends on what you want to teach and where. So, it is hard to answer your questions as the requirements vary from country to country, sometimes school to school, etc.

When I taught overseas, I had personal references, and was not really asked for TESL certification or anything related even though my degrees were NOT in English. My work more than satisfied the university and students, so I suppose you can say I was lucky.

So, perhaps you can try visiting these sites to see if they can give you more perspectives and details.

Top TEFL, TESOL Programs in the United States
http://www.learn4good.com/tefl/tefl_training_usa.htm

Certification and Teacher Training for ESL,EFL,TESOL
http://www.tesol.net/teslprog.teach.html

hope this helps you...and best wishes in your pursuits.