Here are some things I didn't mention in section.  Reading this will
motivate you to study regular expressions and finite automata, and
hopefully help you to understand more about FAs.  This article will
also be linked from my homepage at
http://xcf.berkeley.edu/~alice/cs164-sp99/

Outline
1.  the big picture
2.  more on the difference between DFAs and NFAs

Content
1.  the big picture
Q:  Why do we want to do lexical analysis in the first place?  And why
regular expressions?
A:  The typical programming language constructs are:
  a.  keywords and operators, e.g. "if", "else", "+", "=", etc.
  b.  identifiers, e.g. "i", "j", "num1", "int", etc.
  c.  numbers,
  d.  grouping constructs, e.g. '{', '}', ';', '"', etc.
  e.  quoted strings,
  f.  comments.

  Our first goal in analyzing a program is to give it structure, and 
  thus dividing it up into sizeable little chunks.  This is best 
  achieved by looking for keywords.  The naive method here would be to
  do string comparison between each word in the source program and the
  set of keywords in the programming language.  That would be painfully
  slow.  The less naive method notices that there are patterns in the
  strings of characters.  For instance, a simple description of a number
  would be a string of numbers 0-9, followed by a decimal point, followed
  by another string of numbers.  Thus we develop the notion of regular
  expressions, which concisely describe certain patterns.  There are
  also patterns that regular expressions are powerless to describe.
  An example of non-regular expressions is sequences of balanced
  parentheses.  These will have to be taken care of in the next phase
  of the compiler, with the help of context-free grammars.  We will
  talk about that when we get there.

  DFA/NFA are used to present alternative representations of regular
  expressions.  The reason why we study them in a compilers course
  is because they can be easily translated into programs that
  recognize those patterns.  DFA, NFA, and regular expressions are
  all equivalent in power.  One can freely convert any one of the
  three to the other two, although sometimes going one direction is
  easier than another. 

2.  Difference between DFAs and NFAs
  NFA simulations can be in more than one state at any given time.
  This is a direct result of epsilon-transitions, and multiple
  transitions out of one state on the same input.  In order to 
  convert an NFA to a DFA, one needs to analyze all the possible
  routes through the automaton, and encode them in a new set of
  states and transitions.  The resulting DFA usually has more
  states than NFAs.  This is a classic trade-off between time and
  space.  NFAs take up less space to store, but more time to
  simulate.  DFAs are easy to similate, but are usually less
  intuitive to construct directly, and takes up more space to
  describe.

  Hope this helps.