To teach your cat to sit, place her on a table. Hold the food reward over her head. Say her name and give the command, "Sit." Move the food back over your cat's head. As her head follows the food, she will naturally sit down.
As soon as she sits, make the clicking sound and say, "Sit." Give her the food reward soon after. If your cat does not sit as you move the food over her head, lightly press down on her hindquarters. As you do, continue to hold the food over her head and say "Sit." When she sits, make the clicking sound and give her a food treat.
Soon your cat will begin to associate the food reward with the command and you will no longer have to use the clicker to make her sit. Simply saying "sit" will be enough.
Have you ever tried to get your cat into a carrier when it is time to visit the veterinarian only to find yourself forced into a frustrating game of hide and seek? Teaching your cat to "come" when called makes situations like this one a lot less stressful for both her and you. It's also very helpful if your cat escapes into the yard and you need her to come back home without a major manhunt (cat-hunt).
Once your cat comes to the feeding station at the sound of the clicker, say, "Come," then hit the clicker. When your cat comes, give her some food and praise her.
Continue this process but from other locations around your house. Eventually your cat should come to you reliably when you say "Come!" without you having to click her, though there should always be something worth coming for to reward her.
Teaching your cat to stay is a bit more complex. Place the food down on the floor about ten feet away from her. As she approaches, put your hand out to stop her, say, "Stay," and if she stops, make the clicking sound and reward her. If she keeps on coming, hold your hand out again and repeat the command, "Stay." Reward her only when she stops.
Repeat the process until your cat knows that "Stay" means she should freeze in her tracks.
Training one command may take anything from one or two days to a week or so, so be patient. Make the training sessions fun for your cat and for you and make them something your cat wants to participate in.