The same way I decide which doctor to believe when it's about my own health
or the health of a family member.

Research, research, research. Talking to other (knowledgeable) people (i.e.
nurses, doctors, and so on for human problems, vet techs and vets for pet
problems), reading books, internet materials, going to the library. Etc.

And there's nothing wrong with a good helping of gut instinct, either.
Knowledge is power. Seriously.
No one person can possibly know everything there is to know about their
field. And especially when it comes to the sciences, new things are being
discovered all the time. The more you talk to a variety of doctors (or vets,
as the case may be), the more you're likely to get a good range of
information to base your decisions on.

And the term "correct" isn't always a black and white thing. If an illness or
problem is complicated enough, sometimes each person has part of the answer.  
;)

j...@webtv.net wrote:

You have to use your own judgement and educate yourself.

Depends on how strong you think the people are who gave you the first
and second opinions.

You just have to get a gut feeling about who is being honest and who
has the best qualifications to decide the right path of treatment.  You
should discuss the content of the first opinion with the doctor
offering the second opinion.  You have to educate yourself about the
disease and available treatments.  ultimately *you* have to be the one
to choose a path of treatment, and it is much better to do so by
gathering your own information to make an informed decision.

-L.