Simple system flutes have the same fingering patterns as penny whistles and so if you are already proficient in that instrument you will easily be able to make the jump to flute. Alternatively if you have not played simple system flutes before you might choose to learn penny whistle first, to master the fingerings, and then move on, or perhaps you will learn from scratch on the wooden flute, all are acceptable approaches.
Whichever route you choose, you will need to learn to produce the embouchure when you first pick up the transverse flute. It should be remembered that the shape of the hole produced by your lips when you blow the flute is not round with the lips puckered as when you whistle but rather an almond shape with the lips stretched to the sides to make them as smooth and wrinkle free as possible. You may find that it helps to sit in front of a mirror, without the flute at first, and practise making the shape. You will have to "smile" using the muscles of your cheeks to stretch the lips laterally and turn the lips apart in the middle to produce a thin almond shaped hole which when you blow gently will give a wide thin stream of air. It is good also, at this stage, to practise directing the stream of air up and down by tightening first the upper lip and then the lower lip in turns, this can be felt to be working if you hold the palm of your hand vertically in front of your mouth and feeling the air stream move up and down. It may assist if you push your chin in and out a little at the same time.
Now it is time to pick up the flute. Do not attempt to use the assembled instrument at this stage but only the head joint. Pick up the head joint and block the open end with the palm of your right hand, left hand if you intend to play left handed, you must make an air tight seal, then hold the instrument up to your lips and using the already practised embouchure direct a stream of air at the opposite side of the embouchure hole do not blow too hard, blowing harder will not help. The near side of the hole should be positioned just below your lower lip. If you now roll the head joint in and out you will make a sound try then to stabilise the flute at the point where the sound is produced as the rolling in and out is frowned upon when actually playing. When actually playing you should use your lips to change the direction of the air stream rather than rolling. Continue to practise this till you can pick up the head joint and make a good loud, clear sound first time every time, do not be in too much of a hurry to move on to the next stage as development of a good embouchure technique is essential to good playing.
When you are confident in your basic embouchure technique then add on the body of the flute and try again with all the holes open, this is much easier than starting with all the holes closed. You will find your self producing a different note, practise till it is loud, clear and steady. You can now introduce the fingers one at a time from the top down, take time to get each note properly.
The medieval and Tudor flute was not largely different from the flute we know today.