What is the correct syntax to search a known site for all files witha
specific extension?  I have tried the Advanced search and the synxax
built there does not seem to work (example: rivertown-inc.com
filetype:doc).

Please check your answer by finding all .doc files on
http://rivertown-inc.com.  I have a test file there.

robbjacobs,

There are three Google operators, or special search commands, that you
can use to find specific documents within a specific site:

site: Placing this before a domain name, like site:rivertown-inc.com,
will limit a search to only a specific site.

filetype: Placing this before a file extension, like filetype:doc,
will limit a search to only a specific filetype (in this case, Word
files for .doc)

inurl: If you make a search query with just site: and filetype: 
operators without a search string, you will not get results.  You can
get around this by using this operator, which search pages with only a
specific string of characters in the URL string.  Using inurl:doc (or
inurl: + the filetype you used in the previous operator for the
general case) in addition to the previous two operators will give you
a listing of all documents of a specific type on a specific site.

Using these tools, we will test by searching for all document files on
the IRS government site using this query:

site:irs.gov filetype:doc inurl:doc

This brings up the following results:
://www.google.com/search?q=site%3Airs.gov+filetype%3Adoc+inurl%3Adoc

Unfortunately, a search on your site using these parameters:
site:rivertown-inc.com filetype:doc inurl:doc

Brings up no results.  But I believe this is because you have only
recently added your test file, and it has not yet been spidered and
indexed by Google.  When you can find this page in Google by searching
for it's full URL, you will also be able to find it using this method.

Sites referenced:

Google Operators
://www.google.com/help/operators.html

Filetype Operators
://www.google.com/help/features.html#pdf

Good andwer and easy to understand.  I didn't know that for the syntax
to work, Gogle had to have spidered the site - makes sense.