My wife (and 4 kids) is a Thai citizen and has a Thai passport and is also a U.S. citizen with a U.S. passport.  I understand that MANY others have the same situation and use both passports to travel between LOS and the U.S. wiothout worrying about visas.  Would anyone know the mechanics of their usage?  That is, entering/departing LOS and entering/departing the U.S.A.

You use the passport of that country.  When you exit US use US Passport.  Use again when you re enter the US.  When you arrive Thailand use Thai Passport and use again when you leave Thailand.  When/if asked for your visa you just show them the other passport to prove you do not need a visa.