Tai ji chuan as a martial art
Learn to know what your opponent's intentions are
This is the hardest thing to learn. We always want to either oppose or run away from aggression. The result is that we either break contact entirely. Or we use force to oppose what we think the opponent is trying to do.
Therefore we never even start to listen to what they're doing. Our school teaches various "listening" exercises. They all come under the label - "push hands". The first ones are called the seven pushes. That label is actually misleading. They really should be called "sticky hands" as the idea is to maintain contact with the opponent/partner at all times.
Initially students concentrate on getting the sequence correct. Once they are comfortable with that they can then start to learn to listen. Listening is done with the hands which should be seen as antennae. But one thing is very important. You cannot learn how to do push hands unless you're regularly also practicing the warming-up exercises and the form.
Apply the principles
If your practice combines the warming up exercises, forms practice and push hands you will start applying the principles. Providing your teacher keeps reminding your of them and you learn to remind yourself.
As the principles are more and more integrated as a natural part of your practice your ability to apply them when working with a partner will become almost automatic. But, again, the idea is to persevere. And don't expect to master them - instead be aware of an increased application the longer you are doing Tai ji.
Apply what you learn in everyday situations
This does not mean that you go around picking fights. Rather it means that Tai ji becomes an integrated part of everyday activity. When standing be aware of the separation of substantial and insubstantial. Be aware of the body's structure so that you're aware of the root (below your feet) in your positions. When walking be aware of the shift in weight using the dan tien rather than the upper torso.
Continual "practice" in the above manner will have great benefits. But remember - be patient. Tai ji sneaks up on you.