These can be found numerous places, but I feel they are worth mentioning here. They are on the Yellow/Earth Sash written test, so for my students, you need to memorize the essentials. It also does not hurt to incorporate them into your training.
Following are the Ten Essentials of Tai Chi Chuan Orally transmitted by Yang Chengfu Recorded by Chen Weiming Translated by Jerry Karin
1. Empty, lively, pushing up and energetic1
'Pushing up and energetic' means the posture of the head is upright and straight and the spirit is infused into its apex. You may not use strength. To do so makes the back of the neck stiff, whereupon the chi and blood cannot circulate freely. You must have an intention which is empty, lively (or free) and natural. Without an intention which is empty, lively, pushing up and energetic, you won't be able to raise your spirit.
2. Hold in the chest and pull up the back
The phrase 'hold in the chest' means the chest is slightly reserved inward, which causes the chi to sink to the cinnabar field (dan1 tian2). The chest must not be puffed out. If you do so then the chi is blocked in the chest region, the upper body becomes heavy and lower body light, and it will become easy for the heels to float upward. 'Pulling up the back' makes the chi stick to the back. If you are able to hold in the chest then you will naturally be able to pull up the back. If you can pull up the back, then you will be able to emit a strength from the spine which others cannot oppose.
3. Relax the waist
The waist is the commander of the whole body. Only after you are able to relax the waist2 will the two legs have strength and the lower body be stable. The alternation of empty and full all derive from the turning of the waist. Hence the saying: 'The wellspring of destiny lies in the tiny interstice of the waist. Whenever there is a lack of strength in your form, you must look for it in the waist and legs.
4. Separate empty and full
In the art of Tai Chi Chuan, separating full and empty is the number one rule. If the whole body sits on the right leg, then the right leg is deemed 'full' and the left leg 'empty'. If the whole body sits on the left leg, then the left leg is deemed 'full' and the right leg 'empty'. Only after you are able to distinguish full and empty will turning movements be light, nimble and almost without effort; if you can't distinguish them then your steps will be heavy and sluggish, you won't be able to stand stably, and it will be easy for an opponent to control you.
5. Sink the shoulders and droop the elbows
Sinking the shoulders means the shoulders relax open and hang downward. If you can't relax them downward, the shoulders pop up and then the chi follows and goes upward, causing the whole body to lack strength. Drooping the elbows means the elbows are relaxed downward. If the elbows are elevated then the shoulders are unable to sink. When you use this to push someone they won't go far. It's like the 'cut off' energy of external martial arts3.
6. Use Intent Rather than Force
The taiji classics say, "this is completely a matter of using intent rather than force'. When you practice taijiquan, let the entire body relax and extend. Don't employ even the tiniest amount of coarse strength which would cause musculo-skeletal or circulatory blockage with the result that you restrain or inhibit yourself. Only then will you be able to lightly and nimbly change and transform, circling naturally. Some wonder: if I don't use force, how can I generate force? The net of acupuncture meridians and channels throughout the body are like the waterways on top of the earth. If the waterways are not blocked, the water circulates; if the meridians are not impeded the chi circulates. If you move the body about with stiff force, you swamp the meridians, chi and blood are impeded, movements are not nimble; all someone has to do is begin to guide you and your whole body is moved. If you use intent rather than force, wherever the intent goes, so goes the chi. In this way - because the chi and blood are flowing, circulating every day throughout the entire body, never stagnating - after a lot of practice, you will get true internal strength. That's what the taiji classics mean by "Only by being extremely soft are you able to achieve extreme hardness." Somebody who is really adept at taiji has arms which seem like silk wrapped around iron, immensely heavy. Someone who practices external martial arts, when he is using his force, seems very strong. But when not using force, he is very light and floating. By this we can see that his force is actually external, or superficial strength. The force used by external martial artists is especially easy to lead or deflect, hence it is not of much value.
7. Synchronize Upper and Lower Body
In the taiji classics 'Synchronize Upper and Lower Body is expressed as: "With its root in the foot, emitting from the leg, governed by the waist, manifesting in the hands and fingers - from feet to legs to waist - complete everything in one impulse." * When hands move, the waist moves and legs move, and the gaze moves along with them. Only then can we say the upper and lower body are synchronized. If one part doesn't move then it is not coordinated with the rest.
8. Match Up Inner and Outer
What we are practicing in taiji depends on the spirit, hence the saying: "The spirit is the general, the body his troops". If you can raise your spirit, your movements will naturally be light and nimble, the form nothing more than empty and full, open and closed. When we say 'open', we don't just mean open the arms or legs; the mental intent must open along with the limbs. When we say 'close', we don't just mean close the arms or legs; the mental intent must close along with the limbs. If you can combine inner and outer into a single impulse*, then they become a seamless whole.
9. (Practice) Continuously and Without Interruption
Strength in external martial arts is a kind of acquired, brute force, so it has a beginning and an end, times when it continues and times when it is cut off, such that when the old force is used up and new force hasn't yet arisen, there is a moment when it is extremely easy for the person to be constrained by an opponent. In taiji, we use intent rather than force, and from beginning to end, smoothly and ceaselessly, complete a cycle and return to the beginning, circulating endlessly. That is what the taiji classics mean by "Like the Yangtze or Yellow River, endlessly flowing." And again: "Moving strength is like unreeling silk threads". These both refer to unifying into a single impulse*.
10. Seek Quiescence within Movement
External martial artists prize leaping and stopping as skill, and they do this till breath (chi) and strength are exhausted, so that after practicing they are all out of breath. In taiji we use quiescence to overcome movement, and even in movement, still have quiescence. So when you practice the form, the slower the better! When you do it slowly your breath becomes deep and long, the chi sinks to the cinnabar field (dan1 tian2) and naturally there is no deleterious constriction or enlargement of the blood vessels. If the student tries carefully he may be able to comprehend the meaning behind these words.