Interestingly, the word "disposal" is like "kleenex", "band-aid", "scotch tape", and all the other brand names that have entered the public lexicon.  The word "disposal" is actually a registered trademark for Waste King.  The correct word is garbage disposer.

Or 'garburetor', as they call them in Canada.
 

JAMMED

While trying to wrench a stuck disposal around with the end of a broomstick is the traditional method, an official garbage disposal wrench works a LOT better.  The blades of the tool fit against the blades of the disposal's bottom plate, you give a counterclockwise twist and 9 times out of 10 it'll pop free.  You're then obligated to stick your hand down there and find what caused it to get stuck in the first place.  Most likely a bottle cap or chicken bone.
 

FOUL SMELL

A two-step process: 

Put on some goggles or glasses and slowly pour a gallon of bleach down the drain while the disposal's running.  You might stop a few times and let it soak for a while.

  

With all the grease loosened by the bleach, turn on the disposal and feed two trays of ice cubes into it.  The ice cube shards will act as small knives and slice away the grease.  Don't do it too fast or you'll clog it up, and turn the water on at some point.

 

REPLACEMENT

This usually goes fairly smoothly with one possible hitch.  Older disposals were much wider than the new ones, so if the drain pipe goes from the disposal straight to the wall, it may not be long enough with a thinner disposal and will have to be replaced.

Otherwise, it's just a matter of getting the old one out by unscrewing the three retaining screws under the basin, cleaning everything up, then slipping the new one in.  Use lots of plumber's putty around the drain; it's easy to clean up later.

Also, any electrical wires around water deserve respect, so make sure the new wires are nicely connected and will stay dry.