In Chocolat, how and what does Vianne know about Armande through chocolate?

First of all, keep in mind that Armande is a character who
will do what she wants to do, despite what others think (a fact which infuriates and
eventually alienates her daughter).

It seems, therefore,
that Armande actually sees similar qualities in Vianne when she opens up her
Chocolaterie in a small town right in the middle of Lent.  You asked first in your
question "how."  Well, Armande comes to the shop, and she and Vianne click immediately. 
Through what become fairly regular visits to the shop, Vianne and Armande seal a
wonderful and open friendship.  First, Vianne discovers who Armande's daughter is (a
very religious and pious woman who is ashamed of her mother) and then that Armande does
not have a relationship with her grandson.  Vianne arranges for the two to meet once a
week and read poetry.  It is almost as if Vianne is the daughter Armande never had and
always wanted.

She discovers that Armande has a history
with the priest in town who is laying guilt on all his parishoners for their Lenten
indulgences.  Armande does not attend weekly mass and makes no excuses for
it.

Eventually, and probably too late, Vianne discovers
that Armande suffers from (presumably as I don't believe it is ever mentioned by name)
diabetes, and the indulgences she affords herself in the Chocolaterie are probably
killing her.  Not that knowing would have mattered.  Armande is a woman who does what
she pleases despite and sometimes to spite anyone who gets in her
way.

In the end, the entire family comes together (with
others) to celebrate Armande's birthday.  Armande herself has planned the whole thing,
of course, but it could not have been carried out if it were not for Vianne.  In this
way, Vianne is responsible for bringing Armande together with her grandson and her
daughter - but in doing this - also reconnects Armande's grandson with his
mother.