I live in the Los Angeles area, and I want to become a certied fitness
trainer.  My question is where do I receive the best, and most
thorough training to become a certified fitness trainer in my area?  I
have seen so many companies advertising on line that seem so
fraudulent, I am looking for hands on training rather than on line.

Dear Jasmine, 

The fitness certification field is not regulated, and pratically,
every Joe could form, for example, the "politicalguru-ga fitness
certification programme" and expect you to join, and become a member,
for hefty sums. Therefore, besides my basic advices here, it might be
good to speak with several fitness trainers (from your local Gym, or
even set an appointment with people you don't know, but could help
you) and ask them what places they think would be the best for you. Of
course, always take it for granted, that even those trainers might
have something to benefit by sending you off to a lousy programme,
whose managers paying them (or in which they teach).

Several places offer certification courses in LA area. 

IFPA write in their site, that "There are numerous fitness
certifications, many of which are very good. The best certifications
are scientifically based, have highly qualified instructors, require
continuing education, and are based upon high ethical principles.
Deciding upon the practicality of the certification is also very
important."

They themselves offer numerous courses, and a full list could be
viewed at their site:
http://www.ifpa-fitness.com/Fitness-Certification-Workshops/Fitness_Certification_Workshops_in_California.htm
[You could enlist and get more details in the links bellow the list].

The American Coucil on Exercise holds (this month!) a pilot course in
LA, the prepares for their exam. This course is all sold out (it
begins next week), but they state, that you could contact them for
future details and events:
http://www.acefitness.org/getcertified/gfi_calendar.cfm (Maybe also
going to the course itself and talking with the instructor on the
requirements and their recommendations would help).

The ISSA (International Sport Science Association) seems the most
serious of them all. If you enroll to their certification test, you
could enroll to their seminars, some held in LA:
http://www.issaonline.com/seminars/seminar.cfm 

I hope that helped. Further postings in the misc.fitness discussion
list <http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=UTF-8&group=misc.fitness>
might also help you. I seached for you with terms such as "fitness
trainer", certification, and "lod angeles", to find these programmes
for you. If you need any further clarification on my answer, please
let me know.