According to friends of mine who are Tai Chi practitioners, the most important part of the practice is making sure you are calm and relaxed enough to do the movements. It is crucial to calm your mind, loosen your body, and relax your muscles, joints, and internal organs. Posture is also important, and your body should be naturally straight, so that the crown of your head is lined up with your perineum. To do this, avoid sticking out your chest, stomach, or buttocks, lowering your head, bending your waist, or arching your back. Third, breathe naturally, using the stomach muscle to inhale and exhale, keeping your stomach full and chest empty. Even when turning or moving you should try not to break this posture; your lower body should be steady while your upper body is agile.
Tai Chi movements should be soft, even, and done with ease and agility; do not use muscle power. According to an article I read, movements should follow an arc, with each muscle smoothly, seamlessly moving so movements are linked continuously.
Thanks for sharing these tips. I personally haven't done tai chi in a while but just today saw that I had some old tai chi videos. I think I might try them at some point, as an addition to the yoga I am doing. It's a good practice for your energy as well as to be more body aware.
I also wanted to add that myself (and someone else in my Tai chi class) discovered that our knees would hurt sometimes as early as half an hour into our one hour class. If you are having this type of knee pain and feel the need to shake out your joints after doing a set, you're probably doing it wrong. Bend with your thigh muscles by "sitting" down into your stance, not by bending your knees (which will also classically stick out your butt).
It also may be helpful to keep in mind that your balance and speed should be such that you can stop at any point in the set and hold your position.