Exploring and Climbing
An indoor cat naturally assumes it is permitted anywhere. If you want to keep your cat out of particular places, for example the bedroom of a family member, simply close the door to that area.
If this is not practical, use small heat or motion sensors, available from hardware or security shops. A cat crossing the beam of the sensor activates a high-pitched sound, scaring it of.
These are inexpensive and excellent for training an indoor cat in your absence. For specific locations, such as kitchen work surfaces, double-sided adhesive tape is marvelous: cats hate the sticky feeling under their paws.
Climbing is a natural activity: satisfy your cat's need by providing acceptable indoor locations. For example, placing warm bedding on top of a cupboard acts as an inducement to climb in that area. Use mild indirect punishment to discourage climbing in inappropriate places.
Indirect punishment means your cat does not know it is being reprimanded by you: for example, as your cat starts to climb in a no-go area, make a loud noise by dropping an aluminium soda can with some coins in it, or squirt your cat with a water pistol.
Sensible cats soon associate their activity with these mildly unpleasant consequences. Of course, provide suitable rewards when your cat climbs where you want it to climb.