I need a simple (ie. layman's terms) explanation of what is known as
the Austrian School of Economics (it's not an institution, it's a way
of thinking), or Austrian Economic Theory. I've been able to find
several online articles that reference Austrian economics, and several
organizations that advocate it, but I can't find anything that just
says "People who subscribe to Austrian Economic Theory believe A, B,
and C."

I just need a summary of what it is and how widely accepted it is by
economists and academics.

Hello:

Here is a brief summary of ‘What is Austrian Economic Theory?’ 

First what modern economist of other school of thoughts believes and
than what Austrian economic theory says.

Most modern economist believe that the economy is manipulated by a
vast variety of factors effecting on it. These factors can be
explained by theories and models. Modern economists try to explain
these factors by mathematical and statistical models. Hence, some of
the great economist of the modern era developed their own theories and
methods of evaluating such factors which impact the overall economy.
YOU MIGHT KNOW OF SOME OF THE POPULAR THEORIES OF ECONOMICS.

On contrary, Austrian School of Economics believes that every
individual plays a separate role in shaping the economy. They believe
that although there are some prime factors which are not under the
control of an individual but individuals have the capacity to think
and develop their own logic to achieve something. Therefore, the
behavior and actions of every individual are directed towards
accomplishing some goal. They also believe that there are some
individuals whose actions are capable of changing a society’s economy
single-handedly (example, Bill Gates). Moreover, they argue that the
models presented by the great modern era economists are too mechanical
and the modern economist doesn’t give credit to the human abilities.

The Austrian Economic Theory further explains that every human being
can sense the change in the economic factors and they have the ability
to create change in the factors by putting together their own logic
and judgment. THUS THE INDIVIDUALS DON’T REQUIRE THE MODERN ERA
ECONMIST OF OTHER THOUGHTS TO TELL THEM THAT THE ECONOMY IS INFLUENCED
BY ‘THESE THINGS’ AND THE HUMANS SHOULD ‘DO THIS’ TO ACCOMPLISH
MAXIMUM SUCCESS. Austrian School of economics believes in the
entrepreneurial spirit to derive the economy.

In short, the Austrian School of Economics says that individual human
factor is the largest factor that affects the economy.  And until now
no model can explain the workings of economy to the extent that is
reasonable. BECAUSE ALL THE MODELS ARE TOO MECHANICAL.

As for the acceptance, it is a widely accepted theory. After its
founder, Carl Menger, there have been numerous great names that have
subsequently studied and theorized it. Some of them include Friedrich
von Wieser and Eugen von Böhm-Bawerk. It is a widely accepted
phenomenon and is studied extensively in higher literally economics.

I was able to find one of the pages that clearly (in simple words)
explain what I have just summarized. Here is a link.
http://knight.fcu.edu.tw/~gunning/subjecti/mean_sub/fou_proc.htm

For a detailed description please go to
http://www.mises.org/austecon/chap1.asp

Hope this will work. If you have further questions, please clarify and
I will be obliged to help you on your research. Thanks very much for
providing me an opportunity to answer the question.

Sincerely,
Leader-ga

Thanks, that's exactly what I needed. Someone used the term in a
debate on a message board, and I didnt want to respond until I knew
what it meant. Now I can craft an informed reply. Thanks for your
help!

Just wanted to add a link here from the ever-useful online Concise
Encyclopedia of Economics:

http://www.econlib.org/library/Enc/AustrianEconomics.html

Thanks pafalafa-ga for additional help.

I think it's a bit much to describe Austrian econ. as "widely
accepted".  I've got a lot of time for some aspects of Austrian
theory, but we have to face facts; it is a tiny niche specialty within
academic economics.  There are Austrians at George Mason University,
but I'm not aware of any other prominent economics departments.

Also worth noting that, above and beyond the basic outlook of the
Austrians, well summarised above, they did quite a lot of good work in
capital theory; although Austrian economics is generally not
mathematical, that doesn't mean it isn't rigorous.  Bohm-Bawerk's
theory of long and short term production processes was very good, and
is still influential (in general, the Austrian analysis of capital is
not as a homogeneous factor of production and in my view it is
superior to the neoclassical analysis for this reason).

A lot of Austrian economists were libertarians, which is why a lot of
libertarians (particularly those who frequent internet discussion
boards) like to represent themselves as Austrian economists.  It is
often the case that these people don't understand Austrian economics
and many of them say things which are outright inconsistent with the
Austrians they cite in support (the Mises Institute does nobody any
help by publishing altogether too many of these people).

The most famous contribution of the Austrian School was to the
socialist calculation debate; I would imagine that a google search
would show up some references to that ...

A thoughtful and sympathetic critique:
http://www.gmu.edu/departments/economics/bcaplan/whyaust.htm