I know that the vinyl siding was installed improperly where my decs
meet my house.  I recently replaced a patio door and there was
extensive water damage.  Water gets trapped between the siding and the
deck and house creating a very moist environment.  A friend suggested
I install a piece of pressure treated lumbar between the bottom of the
vinyl siding and top of the deck and seal it with caulk.
What is the proper way to install or finish vinyl siding near a deck
to avoid water damage to the wooden elements (sills, old wooden
siding, etc.) underneath the vinyl siding?

I'm no fan of vinyl siding for exactly the reasons you have
discovered.  There was once a house in my neighborhood (easily 150
years old)  covered completely in vinyl.  New owners bought it and
discovered that everything in the house was rotted.  The house had to
be torn down, thrown in the dumpster and a new house built in its
place.

You must determine where the water is coming from.  Is is coming down
from the roof?  Down from around a upper window?  Leaky plumbing?  Air
conditioner?  Don't assume that is it coming up from the deck. 
Install flashing above window.  Caulk (and maintain that caulk) around
windows and doors.

At every location where the vinyl surronds an opening, make sure that
the top of the opening is flashed so that the water runs outside the
vinyl, not under it.

If the vinyl is covering an earlier siding, consider removing the
vinyl and restoring the original siding that was covered over.  The
cost of periodic scraping and painting will be less in the long run
than having your house rot underneath a plastic cover.