It is said that one of the key teachings of the Professor was that when practising a student should move as if moving in water. After learning the form the next stage is often double handed push hands. This is a two man drill, each person take it in turn to attack and defend. The objective of the drill is to up root your partner. The drill teaches sensitivity and helps develop Root this can be though of as your ability to avoid being pushed over.
Most schools then move on to weapons training.
In a Chen Man Ching style this is usually the double edged sword. The form is equal in length to the hand form and sparring with the sword also takes place. For the advanced student who might be interested in the martial side of the art I would recommend Erle Montaigue's books or videos. I briefly met Erle on a weekend seminar in London, England and can say that he has a very high standard of knowledge and a refreshing willingness to pass it on. The best way to learn Tai Chi or Chi Kung is in a class.