It probably depends on your country and region. I know that in Western Pennsylvania local races and cycling associations regularly seek out volunteers to help officiate the races. For instance, here's an email to the ACA list from this March (I removed names, emails and phone numbers):
The ACA is looking for USAC Officials for our Wednesday Night racing
series in 2013. XXX XXX and XXX XXX are pursuing other opportunities
this season that will keep them from officiating.
Please join me in thanking XXX and XXX for their faithful services
over the last several years. Their professionalism, consistency and
ability to responsibly handle most any situation were a huge asset to
the Allegheny Cycling Association. As is the case with many involved
with the ACA, it is time for others to step up and seize the
opportunity at hand.
For those of you interested, the Official's position is to essentially
run the race. There are two openings available. These are paid
positions ($40 bones a night!). The officials are in charge of the
races. Additional detail on officials responsibilities can be found
here. The commitment runs for twenty two (22) weeks starting April
10th through September 4th. It's OK to miss a night here and there as
we typically have other officials that can fill in. It's a glamorous
job that comes with a car allowance, paid vacation and unfettered
access to ACA celebrities such as XXX XXX, XXX XXX, XXX XXX. Actually,
just kidding on that sentence but I wanted to see who was still
reading. If you really want to hang out with XXX, XXX or XXX we'll
work on that once you're hired.
If you'd like to be considered for the Wednesday Night official
position(s), please contact me directly via email at XXX@gmail.com or
I guess I would find out who runs the races in your region and inquire with them directly. And sign up for their mailing lists.
For this particular offer you may need to be a USAC-recognized officials, but I've seen many announcements for Wardens etc that either did not require an Official's license or included training necessary to get the license. Those requirements are just a google-click away; see http://www.usacycling.org/officials/ for fees, rulebooks and regulations, and, as an example of a training session, http://acccycling.org/news/usa-cycling-officials-clinic/