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Choose a time and place to train your cat. Click and reward. Take your cat's paw. Click, command, and treat. Release the paw and pet the cat. Repeat the process. Wait, then repeat. Command before the click. Reduce the treats over time.
Once your cat has linked the clicker and a treat, pick a time when it is attentive but relaxed. Just before you would normally feed your cat is a particularly good time, because the promise of treats to a hungry cat will sharpen its responses. Work in a peaceful place with few distractions so that the cat concentrates solely on you. Press your clicker and give the cat a treat to remind it of the connection between the clicker and the food. Gently lift one of your cat's front paws. It's a good idea to lift the same paw every time. The cat will learn the trick more easily if you are consistent. While holding the paw in your hand, press your clicker with the other hand, and then give your chosen command-word for the trick, such as "shake." Then give the cat a treat. Release the cat's paw and give it a couple of nice pets. This further reinforces that you are pleased with the cat's behavior, and makes the training experience more pleasurable for the cat. Repeat this cycle as many times as the cat is willing during a period of about five minutes. If the cat spontaneously lifts the correct paw at any time during the training, immediately click, say the command and reward. This sends a strong message that the behavior you require is to lift the paw. You want your cat to enjoy these sessions. If the cat seems uncooperative or disinterested, don't force this issue. Let it wander off and try again another other time. Later in the day, or the next day, repeat the entire process. Lift the cat's paw if it fails to do so on its own, and also immediately click and offer a treat when the cat does it spontaneously. It may take several sessions before your cat starts to raise its paw without you taking it first, and several more before it will do it on command. When the cat starts to frequently lift its paw on its own, try giving the command "shake" without the click. When it places the paw in your hand, then click and reward. The click promises a reward, and the command tells the cat the required action to get it. Your goal is to get the cat to respond to "shake" without the click because it associates the command with a treat. Eventually, it will become unnecessary to give a reward each time the trick is performed. However, do reward the cat at least every three to four times so it doesn't get disheartened. Always conclude each session with a treat. Ending the session with a treat gives the cat consistent, positive reinforcement of the desired behavior.