Push Hand is very important in your Tai Chi training.
The first step to understanding Push Hands is to Develop your Listening Energy (Teng Jing.) Most people make the mistake of bypassing this. Until you can develop your Listening Energy, you will not be able to apply self defense application correctly.
Second step to understanding Push Hand is to develop your understanding of the BaFa.
Afterwards using Teng Jing and BaFa along with Tai Chi foundation you apply the movements of Tai Chi from the 4 Basic forms of Old Frame & New Frame to develop your Self Defense applications. Some of the Self Defense applications include Chin Na to control your opponents.