All you really need is a mat. There are many different kinds of exercise mats, but it is important to use a true yoga mat.
Many exercise mats are thicker than yoga mats. They are often filled with foam or some other cushiony material, and are more than 1/2 inch thick. In yoga, you want your feet to stand on a solid, stable surface. The cushioning in an exercise mat makes it difficult to find and maintain your footing in a yoga pose. So, you don't want to use a surface that you can sink into.
Sometimes, new students are reluctant to invest in a yoga mat before they are sure if they will like yoga. Many yoga studios allow students to "rent" a mat for a small fee per class. If you are taking a class in another type of location, or practicing at home, you will need your own mat.
Yoga mats range in price. If you are just starting out, you can pick up an inexpensive sticky mat at T. J. Maxx, Target, Marshalls, or Wal-Mart. Many yoga studios sell them in their retail areas, as well.
Yoga is best practiced in bare feet. You may see ads for yoga shoes, special yoga socks, and yoga towels. In my opinion, these products are unnecessary, and may even by counterproductive. Your money is better spent paying for a class!