Pay attention when the instructor is teaching techniques or explaining drills. If you're training partner has to reteach what the instructor has shown it is a waste of time.
If you don't understand the technique or need to see it again ask the instructor. This is much more efficient than going off to practice a technique you don't understand and there will probably be other students who also need to see it again.
When you go back with your partner to practice the technique try to do as many repetitions as possible while maintaining good form. Even if you know the technique do as many reps as possible rather than just doing it halfheartedly while having a chat.
Stick to the techniques being taught. Your instructor has chosen to teach these specific techniques in this particular way as he feels this is what will benefit your long term development in Jiujitsu. His choice of what to teach is based on extensive experience. Save your own variations of techniques for open mat and sparring.
Don't 'over-coach' your training partner when drilling. This is usually counterproductive as it will get the student in the habit of not paying attention when the instructor is teaching. Also quite often students teaching other students results in being taught poor or badly understood technique.
Don't try to win in sparring. Work at a controlled pace rather than trying to overpower your training partner. Focus on trying to use the techniques that you have learnt in class rather than seeing it as a strength contest.
If you're paired up with a lower level student don't try to smash them but also don't spend the entire round re-explaining all the concepts and techniques of Jiujitsu. The best and most productive use of the round is to just spar at an acceptable pace allowing them to attempt techniques and letting them get a feel for what Jiujitsu sparring is all about.
Try to roll with a variety of sparring partners in each class. Don't just stick to the same four or five people. A greater variety of sparring partners will give you a better variety of techniques and styles to work against.
Avoid short cuts. There are techniques in Jiujitsu that will allow you to get quick wins in sparring against fellow beginners students however these techniques will not work against anyone who's been training for more than a few months. Think long term and focus on the high percentage techniques that are difficult to pull off now but with consistent practice will be your A game when you're a blue belt or purple belt.
Treat all your training partners with respect. Your training partners are one of the most important elements in how much you will improve. If you treat them well they will want to help you to improve.