The ability to teach or train a cat is one that is often contested.  Some believe that cats will do whatever they like, regardless of the will of their human companion, while others believe that it is entirely possible to train a cat.  Both parties usually have proof of their own to present.  All arguments aside, however, the very nature of the feline is such that training cannot be compared to the training of other animals- especially dogs, who exist in a social hierarchy.  With a cat, you must either dissuade them from an activity that is undesirable by creating an unpleasant circumstance around this activity, or you must reward an activity that is already natural to the cat and which you seek to encourage.  A cat is highly unlikely to learn how to do anything that it doesn't do already, or that it doesn't enjoy doing.   To dissuade a cat...

• Use a water gun to squirt them anytime they misbehave.
• Spray hot-pepper or bitter flavors on items they shouldn't chew or claw.
• Stack non-breakable items that will fall and make a loud noise at the end of counters to keep them from jumping up.
• Use tin-foil, sticky-side up tape or other unpleasant (for paws) coverings to keep them away from an area.
• Use hissing noises when a cat has misbehaved.
• Do not feed them any earlier than you wish to get up.  If they wake you up early in the morning, go for the squirt gun.
• Use the vacuum cleaner as a punishment. (Cat wakes you up to early?  Turn the vacuum on.  Cat on the table?  Time to use the hand vacuum on the table.)