“The success of Yoga does not lie in the ability to perform postures but in how it positively changes the way we live our life and our relationships.”
--T.K.V. Desikachar

Namaste - The divine in me honors the divine in you.

It's called a yoga PRACTICE (not a yoga perfect) for a reason. Focus on what's happening on your own mat without comparing yourself to others, including the teacher.
Listen to your body. If anything hurts, don't do it. If you are confused, observe another student and/or ask the teacher. If you need a break, take one (child's pose is a good posture for resting).
Arrive to class a few minutes early, so you can introduce yourself to the teacher, ask any questions you may have, and share any personal physical issues you may be experiencing.
Silence your cell phone. (Powering it off is even better - a vibrating phone can still be heard in a quite yoga studio.) If your family (or the babysitter) needs a way to reach you in an emergency, leave them with the number of the studio.
Hygiene, hygiene, hygiene. This seems obvious, but worth noting. Be sure your clothing, gear, and person are clean. (Easy DIY mat cleaner = 4 oz spray bottle filled with 2 oz witch hazel, 1 oz water, 2 drops melaleuca/tea tree oil, 1 drop lavender or lemon oil.)
Wear comfortable clothing ... but not too loose or baggy. Layers are helpful. You may want to shed a layer as you warm up through your practice, and then put it back on as you cool down during final relaxation pose (Savasana).
Be open. Your teacher may introduce practice-enhancing breathing techniques, mantras/chants, or more challenging poses. All are optional, but I encourage you to be willing to try new things.
Allow time for yourself. When you arrive, take a moment to settle onto your mat. And allow yourself to relax and enjoy savasana at the end. If you must leave early, let the teacher know in advance, and do so as quickly and quietly as possible.
Bring a water bottle and a towel. Depending on the room and your personal constitution, you may sweat, even in the most gentle or beginner class.
Props. Most yoga studios provide blocks, bolsters, blankets, straps and eye pillows. But a private teacher may not (or may not have enough for everyone), so you may consider bringing your own.