Yoga asana (posture work) is best practised first thing in the morning or early in the evening, around sunset. Morning practice is a great way to revitalize mind and body. Evening practice should incorporate more restful postures, breathing and meditation exercises to help induce a deep, restful sleep. You can drink water before and after class, but as Yoga is best practised on an empty stomach, you should avoid eating a heavy meal 2-3 hours beforehand.
Having said that, it is of course better to fit in your practice whenever you can rather than not practising at all. In the beginning, you may find it difficult to set aside time, but even if you start doing Yoga regularly for 10 minutes a day, it will complement your teacher-led classes and yield benefits. You may find yourself on the path of regular practice sooner than you think.