I recently took on a client who was at one time a very senior person
at a very big company.  Right now, he advises some very very big
companies, and knows a bunch of CEOs personally.  (I'm being fairly
generic in the name of propriety).
 I'm a computer consultant, and he seems to be happy with the work
I've done at his home so far.
 Obviously, this person is well connected.  What I am hoping is that I
can leverage this relationship into something more.  I don't want a
job from anyone, but I would love to get some consulting work, or at
the very least have access to some of the training facilities that
some of the companies he advises has.  As it happens, at least one of
his neighbors is also a client of mine.  This person told me she was
suprised that I knew this guy, but went on to tell me that he was
extremely nice.  (I concurred with what she said.)
 Any ideas on how I can approach this person and see if and/or they can help me?
I'm very honest and straightforward, schmoozing, flattering, BSing,
etc are not strong suits of mine, mostly because I don't engage in
that sort of behavior.