A standard garbage disposal comes with all the hardware required to replace the existing drain in one side of your kitchen sink and connect to the existing drain pipe.
New garbage disposals will come with detailed instructions on exactly how to do this. You can also find specific instructions by looking up the manufacturer of your particular model.
The garbage disposal will first hook up to your stainer, then you have the drain pipe on the side of the disposal which will hook into your p-trap. It is no difference hooking it up with out one. You should have all the pieces all ready there.