I would like to know the proper way to use the title Doctor (DR.) Is
this reserved for Medical Doctors or persons with a PHD also?

Howdy siguy-ga,

The Chicago Manual of Style addresses your question from an editorial
stance in their "Proper Names" Question and Answers (Q&A) section.

"Q. If someone has a PhD and is a professor at a university, what
would be his or her title? Doctor or Professor?"
http://www.press.uchicago.edu/Misc/Chicago/cmosfaq/cmosfaq.ProperNames.html

"'Doctor' is usually reserved for medical doctors, although some
professor use it, and PhD?s who don?t have tenure-track appointments
(and who therefore don?t hold the title of professor) often like to
use 'Doctor' instead."

The University of Texas at Austin website has a "Writer's Style Guide"
that shows the "rights" and "wrongs" of the use of "Dr." for someone
that has their doctorate.

"Do not precede a name with a title of an academic degree and follow
it with the abbreviation for that degree.

Right: Larry R. Faulkner, Ph.D. ...
Right: Dr. Larry R. Faulkner ... 
Wrong: Dr. Larry R. Faulkner, Ph.D ..."

So, yes, one can use the title of Doctor (Dr.) for someone that has a
Ph.D (Philosophiae Doctor or Doctor of Philosophy).  The title is not
reserved for a medical doctor.

If you need any clarification, please feel free to ask.


Search strategy:

Google search on: proper use OR usage "Dr." "Ph.D"
://www.google.com/search?q=proper+use+OR+usage+%22dr.%22+%22Ph.D%22

Looking Forward, denco-ga - Google Answers Researcher

In UK universities, where professorships are far less common than in
the US academic world, the title "Dr" for people with a PhD is very
common. I used to work in a UK government department which, amongst
other things,  collected trade union membership statistics, including
a breakdown into male & female, often this being deduced simply from
the titles members gave themselves (ie Mr, Mrs or Miss). However, the
one union this couldn't be done for was the Association of University
Teachers, because so many members titled themselves Dr, and you
couldn't tell what their gender was.

Siguy-ga,
It depends on where you are (country) and whether you are addressing
the person in writing or orally, or whether you are writing about
them.  I believe that Denco's answer is 100% correct for written usage
in America.
If you are interested in other possible aspects of the question,
please let us know.
Myoarin