Before I start teaching my class of yoga I tune in with the practitioners that joined the class. Have they practiced yoga before, what style, how often and how do they feel today? Are there injuries or any physical problems?
During my hatha classes I often use a similar structure, based of the people who joined the class I adapt a little bit. If someone cares to have a focus on a specific body part, I join in some asanas for those parts.
Yoga is a healing practice where you can use certain asanas or pranayamas to help you feel more certain and comfortable in your body.
During the class I keep an I out on the students, are they doing well? Sometimes people do not have much experience with yoga but they practice sports or pilates and are able to keep up with more advanced postures. When this is the case I always like to put in a bit of extra balancing poses or pranayama and breathing. To also challenge these students a bit.
When I see it is difficult for students to join because they are very stiff, I adapt too. I make a more gentle flow, less sun salutations and more cat cows / sitting down asanas.
It is very important to tune in to your students, what do they need and how to keep them in the perfect balance of a bit of challenge but no over doing!