Say you have a Visa credit card and with it you can accummulate
frequent flyer points and this card is linked to Qantas. Now obviously
the more you spend on your Visa, the more points you would
accummulate. At any time you can redeem your points for plane tickets
with Qantas or any other products with major department stores which
has established a business relationship with Visa. My question is, say
you were to redeem your points for a plane ticket from Brisbane to
Sydney return, now does Visa pay Qantas for a discounted ticket so
that I (the credit card holder) gets the free ticket; or does Qantas
give Visa the free ticket? I would like the answer to state how this
business relationship works between Visa and Qantas similarly with
Visa and other companies whose products through which Visa credit card
users can redeem their points for.

When you use your Visa card, or any credit card for that matter, a
transaction fee (usually 3%) is charged to the merchant.  So that $100
item you just bought, $3 of it went to Visa (that's how Visa makes
money).

Visa takes that $3, and then buys something for you on your behalf. 
In this case, they buy 3 FF miles on your behalf, then insert them
into your account.

3 FF miles probably cost Visa... $0.012.  Literally.  (To give you an
idea of costs for FF miles, go to www.aeroplan.com and under "Collect
Miles", click on "purchase")

Visa in this case doesn't actually "purchase" your ticket, since the
relationship is considered a marketing arrangement where points are
automatically added to your existing Qantas account.  So that plane
ticket you get, you still get from Qantas.