Here’s a video of the exercise number 4.1 from “Exercises for Jazz French Horn”
I have a plan to make some more and better quality videos showing other exercises and playing actual musical phrases. I won’t go into teaching how to do it, because there is plenty of information available on the internet to help you with that.
A good thing to understand is that whenever you take that breath through your nose and puff air out with your cheeks, it affects the sound you’re producing, whether it be intonation or actual sound quality. It’s very, very difficult to take a circular breath without any noticeable change in sound, but we try to minimize it. So that’s the disadvantage. The advantage is, if you’re improvising a long phrase and run out of air, you don’t have to stop! You make these instantaneous decisions on whether it’s more important to maintain your sound quality, or finish your idea.
Have fun!