It's like everything else. Before you learn how to do use it to defend yourself, you have to learn how to do the basics and understand the concepts and mechanics of it. You'll learn how to use the foundational concepts and principals long before you actually learn how to apply the actual techniques. These will actually start to bleed into what you already know.
For example, I suck at Tai Chi push hands, but I practice it enough to where I became more sensitive to the movements of my opponent, and as a result, this helped me greately with my grappling. I could feel where my opponent was weak in structure, so instead of trying to meet force with force, I apply force where there is least resistance. Real world application of this would be. Someone tries to take me down with a single leg or take down, or even a double leg take down. All of their energy is moving forward, so instead of me trying to stop forward movement, I can feel where they aren't pushing. In this case if everything is moving forward then there is no resistance against side way movement, Even better there is no resistance to twisting motion. So instead of sprawling I simply allow my opponent's forward motion while I add twisting motion to it.
See 1:03 on in the video below. Play it at the slowest speed and you'll see me apply this.
The technique that I did wasn't a Tai Chi technique, but I did use what I learned in Yang Tai Chi to know when to start the twisting and how to allow the forward movement to continue. When you watch it in slow motion you can see that the forward movement never stops.