Yoga is an ascetic discipline that originated in the ancient east - it is not known by whom or specifically where - and was later used in early Vedic period India for meditation and a medium for bringing oneself near to achieving nirvana. It also aided in flexibility which would assist them in performing from the book of sexual-spiritual teachings known as the Karma Sutra.  The most common conception of yoga, which, superficially, is correct, is breath control and the adoption of specific bodily poses. However, if you ask any entrant you are guaranteed to receive a much richer philosophical exposition. It has been around for thousands of years and is - next to walking and running - the oldest form of exercise that is still in use in contemporary society.

     There is absolutely no equipment needed in order to engage in yoga. However, the following items are suggested to improve your comfortability and overall satisfaction with the experience. Keep in mind that these are not required and you can use either less or more equipment where it is needed or not needed. 
Yoga Mat: A yoga mat can be anything from a large cushion to a thick blanket, however, visiting your local sport shop or yoga studio and buying a foam mat is recommended as it is cheap, portable and quite comfortable.
Loose, Light Clothing: Wear simple clothing that is light and loose. You do not want to be hampered by irritating drawstrings, itchy fabric, overheating, and other ailments associated with unsuitable clothing. Cotton-linen trousers and top are recommended. They are cheap, comfortable and are the go to garments for yoga aficionados.
Footwear: Footwear is advised against. If you would feel more comfortable or due to an injury or medical condition you are required to wear footwear then that is in no way a problem.
Water Bottle: It is recommended that you have at hand a water bottle. This is to hydrate yourself and keep you focused on the exercise and not your continually increasing state of parchment.
Towel: It is recommended that you bring with you a towel. This is to wipe away sweat and for possible use as a support for the neck, back, or other fragile areas.

If you plan to participate in yoga in your home it is recommended that you acquire an instructional dvd as well as steps, blocks, and straps. If the dvd is part of a package-deal make sure that you look at what equipment you’ll be receiving and if you do not get all of what you want/need then you will have to buy the remaining equipment from a store. If you decide on going to a yoga studio, which is highly recommended, you will have a licensed instructor and more than likely access to all the required equipment. However, calling the studio and making sure that equipment will be supplied is a must.

Techniques

Breathing: The goal of meditating is to reach a state of no-mind. Where you are in a blissful state of being, lamenting not about the past and fearing not the future. It is taught in certain Eastern philosophies that breathing is a way to become in tune with and immersed in the present moment, and this, after all, is the goal of meditation. Yoga is a form of meditation, and breathing, therefore, is of great significance. There are many techniques of breathing that are utilized in yoga, but the most common and the best to start with is deep, slow, rhythmic breaths. Focus on how the air fills your body - the increasing size of the abdomen, the rise of the chest, the full feeling in the diaphagm etc. -  and on the the way it leaves your body - the shrinking and compression of the chest and abdomen, focus on how it affects your mind, how are you feeling at this very moment? - and repeat this indefinitely throughout the entirety of the yoga session. This kind of breathing is intended to bring you to a relaxed state of mind, if this is not the case modify your technique until you reach a state of relaxation. The technique will be different from person to person, do what works for you.
Exertion: Yoga is intended to be a relaxing and meditative experience. This is not a hardcore workout and it will not get you into an amazing physical condition; it will increase your flexibility and your consciousness of your body but will only stimulate your muscles to an infinitesimal extent and burn very few calories. So do not overexert yourself during stretches and poses with the hopes of acquiring that body you’ve been vying for for the past 5 years, it won’t happen. Do not  injure yourself over fallacious beliefs; know the pliable limits of your limbs and slowly work through those limits, thus creating more limits and working through those limits ad infinitum.
Focus: Focus on your breathing; focus on how the breathing is affecting your body; focus on how the poses and stretches are interacting with your muscles - feel the muscle fibers stretching and releasing. Do not focus on what it will feel like if you do this or you you do that, do not focus on what is was like when you did this and you did that, focus on what it is like when you do this and you do that. Bring yourself into the moment and and sustain that state consciousness. 

Safety

I briefly addressed some safety related topics in the previous sub-headings, however it is well worth it to delve a little deeper into some safe practicing techniques that you can utilize in order to minimize your potential for injury and maximize your potential for a fulfilling experience.

Find Yourself a Reputable Instructor: First and foremost find yourself a reputable yoga instructor. This can be in person, on dvd, on the internet, or through any other medium you can find. As long as they are knowledgeable and reputable. Failing to do this essential prerequisite is a very large mistake that can lead to serious injury or, even worse, misinformation, which you may pass on to people in your social sphere and set them up for future injury; creating a ripple of misinformed yoga connoisseurs strutting their soon-to-be-injured-stuff.
Stretch: Yes, during your yoga session you will be stretching continuously, however it is nothing but beneficial to stretch your muscles prior to  starting your session. This can improve blood flow, focus your mind, and loosen your muscles so that once the session starts you will be nicely warmed up and ready - and able - to jump head first into your session; sometimes literally.
Practice Safely: Despite this subheading bringing to mind obvious sex-ed reminiscences, this is a serious matter - unlike elementary sex-ed - and it is vital that you practice yoga safely. Breaking through limits is infinitely important. It can boost self esteem, increase your passion and deepen your immersion into yogas subculture - all of which have their own benefits and those benefits their own benefits etc. - but what is the point of breaking through your limits if you simultaneously break yourself? Other than a interim of an elevated ego and a possibly educational trip the hospital there are, we can agree, very few. If you feel sharp pain - do not confuse discomfort with sharp pain, discomfort is a natural occurrence during physical exercise - whilst performing a yoga pose,  stop. Readjust. And carry on. Practice breaking through your limits gradually. It will save you a lot of time, money, and self-confidence.
Diet: This is not so much a safety tip as opposed to a word of warning. Never eat foods that are unfamiliar to you before any kind of workout, it can irritate your stomach, distract you and break your focus, and make a very uncomfortable and potentially messy scene. So please, for the benefit of the group, stick to familiar foods before working out and experiment with exotic cuisine on your days off. It will be sincerely appreciated.

Sources For More Information

If, after reading this, you are interested in learning more about yoga, it is advised that you do some external research on the internet. Below are some links that can start you on your way.

http://breakingmuscle.com/yoga/how-to-practice-safe-yoga

http://www.medicinenet.com/yoga/page6.htm

http://iml.jou.ufl.edu/projects/fall05/levy/history.html