Commercial air conditioners and central air conditioning units should only be moved by a licensed air conditioner repair firm that can safely disconnect coolant lines. Air conditioners contain coolant that can be harmful if allowed to leak out.
Angie's List or your local Yellow Pages should have listings of licensed and bonded air conditioner repair companies. Portable window unit air conditioners just need to be unplugged and pulled out of the window before being moved to another window. Air conditioners should remain upright when they are moved. Large window unit air conditioners require several people to move, possibly with a hand truck.
Take care to not damage the condenser coils. Never grab an air conditioner by the condenser coils or lay it down so that the coils can be smashed. If you are moving to a different home and want to take your air conditioner with you, then make sure to remove the filter and pack it well in a box padded with old newspaper or bubble wrap. Most people do not move a central air conditioning unit once it is installed, since a technician must do this. Usually, outdoor AC units are only moved if a home expansion or renovation requires it.