If you are referring to someone who experienced a heart attack. Would
the right English when explaining to someone be: He or She "took a
heart attack"? or He or She had a heart attack?

Although, in colloquial English, you can say that a person "took
sick," I don't believe I have ever heard anyone say that someone "took
a heart attack."

Pinkfreud is correct.  

The only time the word "took" would be appropriate would be in a
sentence such as this:

?My doctor ignored my heart scan. It took a heart attack to prove him wrong!?
http://www.prleap.com/pr/27450/

Although I think "took a heart attack" sounds bizarre, some might find
it to be technically acceptable. I found this in Merriam-Webster's
Unabridged Dictionary (CD-ROM edition):

"take...
to strike or affect so as to cause to be in a particular condition
<was taken ill> <found himself taken hoarse> <was taken down with
pneumonia>"

Maybe, but I don't think that helps someone learning English.  It just
is NOT standard English usage to say:  "I took a heart attack."

There is something in the language that suggests that illnesses come
from outside the body, as infectious diseases do.  "One catches the
flu or a cold or measles." Or: "One is taken ill," passive voice, the
illness takes/overcomes one.
Other afflictions from within the person's body are just there, one
"has" them:  a heart attack, a tumor, cancer, a stroke.

So:  "He had a heart attack."

(Now someone explain why we say  "the flu", "a cold", but "measles"
with no article.)  :-?

Myoarin...

We say measles because measles are considered plural...eg: many red spots ;)

Steph53

Thanks Steph.  I feel some red spots, myself.  Actually, we say:  "He
caught the measles."  Otherwise, I would agree with you; it is or
sounds plural.
Myo