Holding The Flute
Right handed players should have their left hand to nearest the mouth piece, right to bottom. Left handed players the reverse. Although, I am left handed and play right handed. This really is a personal preference and depends on what feels more natural to you. You should remember this when purchasing a flute. Sometimes the holes are offset in a slight curve to cater for the finger positions of the hand which will be covering them. It would be very awkward trying to play a right handed flute as a left handed player. I believe it’s easier to buy right handed flutes than left, unless you have you’re flutes custom made; which is actually a normal thing to do (see buying).

Hand positions
Thumbs should be placed on the centre at the back of the flute. Left thumb just above the first hole. Right an inch above the fourth hole. It can be beneficial to place, and keep, your little fingers on flute. This helps stabilize the flute when releasing all of the other fingers(advanced). This is however easier said than done and I keep forgetting to do it. This really depends on the range of notes you are confortable playing. As you progress you will start to include additional notes which will be much easier played using the little finger to support the flute.
Thumb positions