How do I begin the process of selling clothing (wrist warmers) to the
US armed forces?  I'm looking for a department that is in charge of
procurement for each and every branch, including the US Coast Guard.

Hi! Thanks for the question.

The US Department of Defense is the central department you should
concern yourself whenever you want to sell anything to the Army, Navy
and to other departments. Our first link provides a document detailing
the process and steps you will need to undertake so as to sell to the
military. Here are some steps:

a. For purchases within $100,000 or less: ?Most of these millions of
actions are accomplished using simplified acquisition procedures. Oral
solicitations or very brief written requests for quotations are issued
to prospective suppliers in the local purchasing area. The successful
quoter is issued a purchase order, and compliance with the order
(i.e., delivering the product or performing the service) constitutes
contract acceptance and fulfillment.?

b. Above $100,000: ??made by sealed bidding by competitive proposals,
or (in unusual circumstances only) by other-than-competitive
procedures.?

c. ?Procurement by sealed bidding begins with the issuance of an
invitation for bids (IFB) containing all the information bidders need
to respond.?

d. ?When sealed bids are not appropriate, competitive proposals are solicited.?

?Selling to the Military: How to Get Started?
http://www.acq.osd.mil/sadbu/publications/selling/part1.htm  


Our next article provides information on the different Military
Purchasing offices. Furthermore, this page includes the product
categories bought by the DOD.

?PART 2:  PRODUCTS AND SERVICES BOUGHT BY MAJOR MILITARY PURCHASING OFFICES?
http://www.acq.osd.mil/sadbu/publications/selling/part2.htm 


Our next link provides the whole booklet of selling to the DOD and
other related agencies. Please read this in full since it provides
additional valuable information. I separated the first two parts above
since they are the most imperative resources for your concerns.

?Selling to the Military?
http://www.acq.osd.mil/sadbu/publications/selling/index.html 


--------------------------
The US Coast Guard meanwhile is part of the related agency called the
Department of Homeland Security. Here is the contact information for
the purchasing department of the Coast Guard.

U.S. Coast Guard
Office of Procurement Management 
2100 2nd Street, SW
Room 2606
Washington, DC
20593-0001 

Phyllis Miriashtiani (G-CPM-S/1), 
Small Business Program Manager
(202) 267-1172
pmiriashtiani@comdt.uscg.mil


You can get the contact information for the other business departments
of the Coast Guard and other agencies of the Department of Homeland
Security from our next link: (You will need Microsoft Word for this)

?Small Business Specialist?
http://www.dhs.gov/dhspublic/interweb/assetlibrary/DHSOSDBUlist2.doc 


Just like the Department of Defense, the Department of Homeland
Security also has a discussion of the necessary steps to undertake to
help you in selling your product.

?Working with DHS?
http://www.dhs.gov/dhspublic/interapp/editorial/editorial_0421.xml 


Search terms used:
US Armed Forces procurement
US "coast Guard" purchase

I hope these links would help you in your research. Before rating this
answer, please ask for a clarification if you have a question or if
you would need further information.
                 
Thanks for visiting us.                
                 
Regards,                 
Easterangel-ga                 
Google Answers Researcher

www.fedopps.com holds up-to-date US government contract information
from hundreds of government bodies including the armed forces.

You can sign-up for a 5 day demo. During the trial period you can
search all government bids published in the last 6 months. You should
also take some time to build your "profile" which will then be used to
automatically locate new contracts that might be of interest and they
will be emailed to you.

You should also find lots of useful information to help you win a
contract once you've found it. And if you don't find the information
you are looking for the staff that run the site should be able to help
you further.

Good luck!