How can microarrays be used to quantitatively determine level of gene expression?
From the comments:

MattDMo:


  You can compare different samples, which may have started out as
  different amounts of tissue, by using control genes. The numbers
  reported by most standard microarray experiments are not absolutely
  quantitative (There are 2450 copies of this RNA per cell in this
  sample), but are rather a proportion as compared to a set of
  housekeeping genes whose levels are not expected to vary much between
  the samples you are analyzing.


cagliari2005:


  For PCR amplification, you are right, this is a random process and
  while you would expect most RNAs to be similarly amplified, biases can
  and will occur. Amplification biases are usually assumed to be
  identical between similar samples and therefore will (mostly) cancel
  out during the differential analysis.