There are two parts to replacing an old garbage disposal unit: First is the unit itself and second is the electrical supply. Replacing a unit is surprisingly easy. If you have one of the main brands from WasteKing or Insinkerator, they have standardised twist and lock fittings - simply twist off the old unit and twist and lock on the new unit under your sink. If you're changing from one brand to another, there are adapters that simply bolt on under your sink.
For the electrical side, you should turn to a qualified (and certified) electrician. Often, these units simply plug into a wall socket under the sink, in which case it's easy. However, many are hard-wired in to a wall adapter with an RCD short-circuit protector and these need to be fitted by a professional.
Hope this helps!