My clients love the emphasis on breathing, both throughout the workout and at the end! It seems odd that such a thing would bring about so much satisfaction, but I think it stems from the fact that most people nowadays breathe very shallowly (is that even a word??). I encourage deep breaths (deep, slow inhales and exhales) and belly breaths, where appropriate during the workout, and incorporate stretching, torso rotations, and head tilts (front, back, side to side, and over shoulders) at the end of the session. Funny, I've had so many people remark that it's the only time during their day where they actually stop, breathe, and relax; and they LOVE it!!
Teaching people to BREATHE is one of the main components of any session I am conducting. Once I have them conscious of how they are breathing, I teach them one or of the following: relaxation breathing diaphragmatic breathing, Uji breathing to utilize during the session. At the end of the session, I encourage a relaxation breathe and the simple awareness of where the breathe is coming from in the body.
In teach my clients to breathe constatly. i don´t tell them when to inhale or exhale. Just to keep breathing while exercising.
It can greatly depend on the work out. Different types of yoga have different breathing techniques. Ashtanga yoga often has you breathe in and out through the nose only.
One thing that I like to focus on is helping my clients relax. At the end of our workouts, I have my clients lay flat on their backs on a mat, close their eyes and perform deep "belly" breathing (deep breath in through their noses, release slowly out the mouth). While performing this, I talk to them in a relaxed tone and ask them to visualize certain things (depending on what some of their goals or other things important in their lives are). I use this a lot with my athletes, but also very successfully with regular fitness clients. It always amazes me to see how relaxed this short breathing session will help the client become.
For most exercises I teach my clientele to breath as natural as possible but I do show them how to stabalize their torso with fully inflated lungs and how to increase flexion by deflating their lungs. The last two are very short term motions but highly beneficial to safety and progress.