Your cat can communicate in many different ways -- through vocalizations, touch, and body language.
Her whiskers can be used in a form of gentle greeting with another cat. Cats also release scent through touch that claims people and things and their territory. If your cat butts you with her head and rubs her cheek and neck against you, she is leaving behind a special scent to mark you.
Vocalizations vary from cat to cat. Some breeds, like the Siamese, are known for being chatty, and will often "talk" to their family. Other breeds are mostly quiet. As you get to know your cat over time, you will learn what the different sounds mean. Your cat may meow when she is hungry, content, or playful. Purring generally indicates contentment. Hissing, spitting, and snarling are expressions of fear, anger, or dissatisfaction. Yowling is a cat-to-cat communication, and is often a cry of the female in heat.
Your cat's body language can tell you a lot about her mood. A happy, content cat at rest will be relaxed, but alert. Her ears will be erect and her whiskers will be relaxed. A very content cat may knead the surface she is resting on, a favorite cushion or an owner's lap!
A cat that is ready to fight will try to make herself seem as large as possible. The fur along her spine will stand on end, and she may arch her back. Her eyes will be narrowed to slits and her ears will lay flat back. Her whiskers will stretch forward.
Flattened ears can also be a sign of fear, especially when combined with flattened whiskers. The eyes of a fearful cat will be wide.
Keep in mind that your cat's body language and vocalizations may differ. Every cat has his or her own personality that will show through over time. Whether you've got a chatty cat or a silent one, you will learn your cat's moods and develop your own special way of communicating.