I have read that you can now request a free copy of your credit report
once a year thanks to the Fair and Accurate Credit Transactions Act of 2003.

Source: http://www.creditchampion.com/default.asp?S=AC3&Document=Credit+Reports

How do I go about getting this?  Should I just cold-call the big-three
credit agencies?

I live in Washington State.

Unfortunately, loopholes in that provision of the  law mean that it
hasn't really taken effect yet:
http://credit.about.com/gi/dynamic/offsite.htm?zi=1/XJ&sdn=credit&zu=http%3A%2F%2Fwww.bankrate.com%2Fbrm%2Fnews%2Fcc%2F20031223a1.asp

Regards,

aceresearcher

Howdy palmquasi-ga,

According to this Federal Trade Commission (FTC) article, you will have to
wait until the end of this year.
http://www.ftc.gov/opa/2004/03/facta.htm

"Congress has directed the FTC to ... to establish a 'centralized source'
...
The centralized source is intended to enable consumers to order all three
reports at one time. The FTC?s proposed rule requires that the centralized
source for free credit report requests to the three nationwide CRAs be
available to consumers through an Internet Web site, a toll-free telephone
number, and a postal address.
...
The FTC proposes a cumulative, regional roll-out over nine months, from
west to east, beginning December 1, 2004. Under this plan, consumers will
become eligible on the following schedule: (... Washington ...) ..."

If this suffices as an Answer to your Question, I will be happy to post
it as such.

Looking Forward, denco-ga - Google Answers Researcher

If you visit each website (transunion, experian, equifax) you can
request them to mail it to you at no charge (once per year or if you
are denied employment).  One has it available online for free, but I
believe the others require the free ones to be mailed.  They will try
to sell you one, but if you dig around thier sites the free one will
be there.

Regarding the Comment:
<< If you visit each website (transunion, experian, equifax) you can
request them to mail it to you at no charge (once per year or if you
are denied employment). >>
This is only true if you fall under one of the provisions listed below.

"In fact, by law you are required access to a free copy within 60 days
of being turn down for credit. Find out which credit bureau turned you
down and make your request. Additionally you are entitled to a free
copy annually from any bureau if you live in the states of Colorado,
Georgia [2 per year], Maryland, Massachusetts, New Jersey, or Vermont.
You can also get a copy if unemployed and applying for a job within 60
days (include a copy of an unemployment check or layoff notice). If
you are on public assistance you can also get a free copy (enclose
proof with your request). If you believe you are a victim of fraud
(include letter of circumstances), you can get a copy as well. Of
course you can get a copy at anytime at cost from $2 to $8 depending
upon your state."
http://credit.about.com/cs/creditrepair/a/042701.htm

Regards,

aceresearcher