Pilates is an excercise for the core muscles. OK, enough about that, you can look up that stuff on you own.
What you need to get started is a mat about 1/2 inch or thicker.
Pilates involves lying on your back, kneeling, rolling and other excercises that require a thick mat.
Don't use a Yoga mat, they are usually too thin.
Yoga mats are designed to keep you from slipping and to feel the floor with your feet and hands.
Pilates is usually done barefoot to allow foot to flex.
The only other item you might want is an excercise ball. We'll do lots of excercises on the ball.
They come in different sizes and colors. Get one for your height and try to get a cool color.
Thats about all you need to know. Now go do some Pilates