Holding the flute 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 four points that you make contact with the flute that help with the balance:
All three 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 flute rest on the thumb.
Below is a picture showing you where to put your fingers.
Next, lets go to posture.