The concept of circular breathing is kind of a tricky one to explain. It's kind of like riding a bike in that when you know how to do it, you're going to know how to do it forever. It's quite tricky to actually get there. The concept basically in a nutshell is to form a pocket of air in your mouth, like that, and to close off your throat so you're not breathing. You're not connected to your lungs anymore. The air in your mouth is not connected to your lungs. And you just push it out like that. While you're doing that, you breathe in through your nose and refill your lungs. Sounds really tricky, but if you can slow down the time it takes for the pocket of air in your mouth the empty, it gives you more time to breath and start the air flow again smoothly. That gives you a good amount of time.
The best way to practice this away from a didgeridoo is to sit yourself down with a scotch glass and a straw and some water, and just try to keep the bubbles consistent by doing that. That can go on forever. When we get to the saxophone, we take something that we already know like long tones and just try to keep the tone consistent. That's how you circular breathe.