I have tried using my Direct TV Satellite System in various areas of
the country.  When I set-up somewhere other than near the area where
my local stations operate, the system knows I am not where I should be
and will not let me watch those local channels.  I am not using the
phone line, so the system must be able to determine my approximate
location from the satellite signal itself.  How does it do this?  (I'm
sure there is no GPS etc. involved).

Hello Bushman,

Based on what I can find, DirecTV uses "spot beams" to transmit the
local channels to each area for local channels. This is described in a
number of sites including:

DirecTV orders high power satellite (report in 12/99, launched in
2001)
http://spaceflightnow.com/news/9912/11directv4sorder/
Second spot satellite order
http://spaceflightnow.com/news/n0109/09direct7s/
News of upcoming launch
http://www.spacedaily.com/news/satellite-biz-01za.html
Post launch news
http://www.hughes.com/ir/pr/01_11_26_spotbeam.xml

As a result, you can't find the local channels outside of your local
area because the signal is not there to be received. The only
exceptions are the Los Angeles and New York channels broadcast for the
areas that do not have local channel service.

I found this using a search with
  directv local channels
  directv local channels spot beam

Let me know if you need additional details on this answer.
  --Maniac

Maniac.  I think you've got it!  I did some searches too and just
couldn't find the answer. Thank you.