Holding the clarinet is a very important first step that all young students need to carefully work at. Hand positioning greatly affects how you play, so it is important to master it early on. There are two points that you make contact with the clarinet that help with the balance:
Both points are very important, but pay close attention to your right hand. Think about your right thumb as a brace rather than holding the instrument. Just let the clarinet rest on the thumb.
Look at the images below to show you where to put your fingers.
Next, lets go to posture.