How is garbage disposal installation different in a sink without an existing disposal?
Most installation kits will come with the replacement sink basket that the disposer will mount to.  You'll need plumber's putty to seal the basket as you install it.  Typically it is just a nut or snap ring. 

Some of the drain pipes will need to be rearranged to connect to the offset outlet on the disposer.  This is basic plumbing, and with patience an a few trips to a hardware store can generally be done.  Do not permanently remove the waste trap.  The work can difficult without experience, consult a good book on plumbing or hire a licensed plumber.  You will also need electrical power and a switch for the unit, which may require a licensed electrician.

Also sewer districts have been making rulings about the use of disposers in their jurisdictions.  Some encourage their use, most are starting to discourage or ban units.