Whenever I do asanas that involve me putting body weight over my hands, my wrists start paining and I am unable to sustain the posture for long. What should I do?

As you progress in the journey of yoga you will gain the strength to carry your body weight. In the meantime, please do as much as you comfortably can and take a break and rest whenever there is pain. Remember, it is a journey and slowly and gradually you will see improvements. You can some basic wrist movements before the yoga class starts along with your warm up. Wrist6 rotations and stretches on the mat.