You can tell cats are very smart just by watching them for a few minutes. They are quick learners and have thousands of years of evolution behind their abilities to observe and make intelligent decisions based on what they sense. Try to understand how they think and you'll deepen your connection to your pet. Here are three key characteristics:
What's in it for me?
A dog may thrive on finding opportunities to please you, but do not expect the same from your cat. Cats find much of their motivation in discovering the sources of personal benefit. They decide what they'll do and when based on what it gets them. For example, you may think your cat comes when called out of obedience, but your habit of handing out a few kibbles of cat food as a treat is more likely the reason.
The fine art of imitation.
Generally speaking, cats are smart enough to take advantage of your habits and routines. They will train you at every opportunity. If your cat recognises that you're always willing to get out of bed and feed her when she makes noise, you can count on her making noise night after night.
When existing pets, especially cats, and the new cat start showing a healthy curiosity toward each other, it's time to give them a chance to get a little closer.