1.) Practice! The point of a private lesson is to gain new insight into both the pieces you're learning and the instrument you play. If you don't practice between lessons, you force your teacher to reiterate advice already given and to work with you on assignments that should have been done on your own time.
NOTE: This is not the same as practicing something with a concerted effort and remaining confused; this is normal and completely fine, especially when you're learning a new concept. But not touching your instrument between lessons is a waste of your money and everyone's time.
2.) Use lip balm frequently and liberally throughout the week. Chapped, cracked lips create an unfocused air stream, which in turn produces a fuzzy sound.
3.) Warm up on your own time! Do scales, long tones, and articulation exercises in all registers before your lesson starts so that your muscles will be prepared and responsive during your lesson. Don't make your teacher take time out of your lesson for warmups; this takes away from time that could be spent working on your music.
4.) Drink plenty of water. Dehydration leads to cracked lips and dry mouth, both of which interfere with sound production.
5.) Eat, but not too close to lesson time. It's hard to teach students who are full to bursting and can't take a full breath, but it's equally hard to keep students focused when their blood sugar is low. Give yourself at least an hour to digest before your lesson time.
6.) Take notes during your daily practice time. You probably won't remember all the observations you make or questions that arise over the course of a week, but sharing these with your teacher makes for extra-productive lessons. You relieve your teacher of the burden of trying to guess what you struggle with, which is different for each person. Even good teachers aren't mind readers; if you are having an issue that isn't readily obvious, such as joint pain or incomplete understanding of a concept, take some notes about it and bring them to your lesson.
7.) Take notes during your lesson. A lot of information is presented and assignments are given, so unless you have superhuman memory, write down some reminders for yourself as your teacher talks.
8.) Ask questions! If you don't understand or want to know more, don't be afraid to speak up. Questions are a sign of an engaged, attentive student and I personally enjoy when my students ask me things about what we're studying. Don't just save it for the lesson, either; if you really need to clarify something in order to get work done that week, email or call your teacher. It's much better to do that than to lose a week of practice time and walk into your lesson with minimal progress made.
9.) Pay attention when your teacher is talking. Assuming your teacher is qualified, what they have to say during your lessons will be valuable and helpful to you when you practice on your own during the week. You're paying to be there, so why not listen up?
10.) Be open to constructive criticism. You're studying with your teacher because you have more to learn, not because you know everything already.