What documents do
I need to have when applying for a TEFL job?
Should I
send originals to the potential employer?

You
will, of course, need a passport. If you have received
a degree, make sure you have it - and sealed
(official) transcripts.
If
you have taken any kind of TEFL training, have your
certificate(s)/diploma(s) ready. Prepare a good generic
cover letter to change for each specific employer. Keep
copies of your resume handy as well.
Copies, not Originals
Employers will ask for your documents in the application
process. Try not to send originals - certainly not in
the early stages. There will be times once you are
offered - and have accepted - a position when you may
need to part with your originals. If at all possible, do
not part with originals - send the copies.
Avoid Blackmail
Some potential employers may ask for your documents,
pending your hire, and then significantly change their
offer, once they have all your originals. Some will
claim to have "lost" your documents. Don't allow
yourself to get caught in such a situation. Every
university and most TEFL schools will be happy to issue,
for a reasonable fee - additional originals.
Order and keep spare copies of your transcripts as well
(if you have a degree). Sure, the cost adds up a bit -
but you will never be stuck or held hostage by an
employer.
I
keep extra originals of everything. Who knows? I might
accept a couple job offers at one time some day, and
take the one that really comes through.
Passport
Just my opinion - but never give your passport to
anyone except an embassy or immigration official. That
said, there may be times when you might need to do so.
Just keep track of who has it, why, and how long it will
be until you get it back. When I worked in Saudi Arabia
- it was standard for your employer to hold your
passport. Kind of weird and scary - but so it was. You
could either quit or give it to them. I chose to give
it to them and save some serious money for five years.
Other Documents
Such an odd array of things can be asked of you, that it
is hard to completely prepare ahead of time. You may be
asked for a local police clearance (that you are not
"wanted") or a wide variety of medical clearances (many
of which you will just have to do again when you get
there!).
Be
patient, provide what they ask, it will all work out.
You won't be the first person to be scared or
intimidated by the mountain of paperwork required.
Personally, I always wonder if I can get through all of
it! But I always do.