There is a defined course in Tai Chi Chuan training that is followed by most traditional schools.
The first step is training for force and skill.
This is the place everyone in any martial art needs to begin. Here we work on health and fitness. In Tai Chi we learn Qigong as a basic training method. Usually a moving qigong is taught first, then a static one called Zhan Zhuang or standing post is taught next. Then we move onto skills such as learning to unify the body to manifest what in Taijiquan we call Chan Si Jing, or silk reeling strength. This is a way of learning to move from the feet, through the legs, to the arms. We take the time to relax and unify the body as one whole unit. After this we begin practicing exercises for flexibility. We begin breathing and stretching rhythmically. Perhaps my favorite example of this ind of training comes as a story from the Tai Chi Master Kuo Lien Ying who spoke of how in the old days his teachers before him would insist you practice stretching until you could put your teeth to your toe. After these skills are trained then the students begins to learn individual movements from a Tai Chi form.
There is a saying that I have heard over and over again throughout my years of learning Tai Chi: Until you have practiced a movement 5000 times, you do not own it.
This is very true. This repetitive practice of the same movements over and over may seem boring but with a good teacher you will learn how to breathe, how to move mind and energy, how to manifest power from this portion of the training.
After you have reached a standard that the teacher is pleased with (note that in Asia it is unthinkable to ever tell your Sifu that you "know something already" if he or she is a good teacher then trust that this is not a stalling tactic but a time to refine movements and sensations.) your teacher will then begin to teach you the form. The form is an extended qigong exercise, a concise encapsulation of highly effective combat techniques, and a moving meditation. However, for it to be these things, you must have followed the training schedule and have already developed force and skill. Without force and skill your form is an empty dance or as the Chinese saying goes "Brocade legs and flowery fists." You would probably get more benefit from going to a swing dance class if you only practice form.
After the form is learned we move onto Tui Shou or Pushing Hands exercises. This work is done with a partner to help teach you distance, timing, and the application of force in a safe, controlled environment. Eventually the push hands becomes a freestyle affair, but you need the proper foundation learned in the basics to make it to that point.
After Push Hands you will move on to learn a weapon form or two to teach you how to project your energy past your physical body. Then you will spend much time learning applications in prearranged sparring patterns until finally we reach the stage of San Shou or free hands wherein you can fight freely and creatively with the techniques, principles, and movements you have learned.
So there you have it. The proper way to learn Tai Chi. Anything else is as TT Liang once said: A blind alley.