where can I find a newspaper article from around December 18th, 1956 in
vancouver canada?

Do you know the name of the newspaper, and/or what the article title
was or was about?

If so, a researcher may be able to find out if the paper is indexed
online (usually only major newspapers currently have this available,
for a subscription).  Otherwise they may be able to tell you the
location of the old newspapers (libraries, the newpaper's own
archives, etc.)  If it is the latter, then you can request a photocopy
of the article either through your own home libary's interlibrary loan
office or sometimes the owning library has a document delivery
service.  But in any case part or all of the article title may have to
be known and the name of the paper of course.

Hopefully this helps.  You can also go to the Vancouver Public Library
(main) at Georgia & Hamilton.  I forgot what floor it's on, but the
library keeps a record of every Vancouver Sun and Province that has
been published and can be viewed at anytime.

It's unlikely that you'll ever find any newspaper article published
before the late 1980's online. Because that is when papers began
printing using a digital format, instead the old fashioned
typesetting. It would be too costly and time consuming to scan papers
published before then.

As has already been pointed out, you best bet would be to contact
either the newspaper directly or the Vancouver Public Library

Actually a lot of newspapers are beginning to scan the old copies. 
For instance the Chicago Tribune has fully searchable archives back to
1876.