Music notation is the art, science, and practice of describing music in some written form. The most common form of Music notation originated in the 12th century as a way to record both pitch and duration of words chanted by monks. This notation has evolved into the modern European system with its musical staff of five lines, with its black dots and circles representing notes. But there are other schemes for notating music, and they are called 'Tablature', which is commonly shortened to 'Tab'. And they approach describing music in subtly different way.
The modern European system approaches notation by recording what is heard, instead of how it is played. For example, you hear a 'G' then you write a little note on the G line of the musical staff. It is the responsibility of the performer, to recognize that 'G' and then know how a 'G' is played on their instrument. And if they change to an instrument of a different pitch, then the performer has to know how to play 'G' on this different instrument. Although there are some advantages to this approach, many find this entirely too complicated, that it gets in the way of their playing.
Tablature is simpler because it records how something is played. For example on string instruments the notation would record which string to pluck and which fret the string is held against. With flutes, tablature records which fingering to use without regard to the fundamental pitch of the instrument.
There are two popular systems for recording flute music. One is fingering guides, they are just little pictures of flutes showing which holes are covered or not. Unfortunately, finger guides only record the pitches of a melody and not their duration and rhythm. R. Carlos Nakai developed 'Nakai Tablature' which reuses much of rhythm notation from the modern European system, but simplifies how pitch is handled. Instead of a note on the staff representing a pitch, they directly represent a fingering, no matter what the fundamental pitch of the instrument. This requires learning one finger position for each note that appears on the staff. For example, the note on the first space of the staff is played by covering all six holes. So to read 'Nakai Tablature', one needs to understand duration as any musician does and memorize the fingering for a few notes.
'Nakai Tablature' pretty much works with 'contemporary' Native American flutes, which have been created with electronic tuners and with the popular minor scale. It should be noted that the "contemporary" makers have diverged a little bit on their suggested fingerings from the original "Nakai Tablature". This is the result of different makers optimizing their flutes in subtle ways to be easier to play, or better in tune, or appear more traditional. Each improvement of one aspect tends to compromise the other aspects. But the basic fingering is about the same on all such flutes. This contrasts with historic flutes of the prior century with their greatly varied tuning and indigenous scales. These old flutes many not reproduced melodies in a desirable fashion when played with same fingering as the 'contemporary' flutes. The same could also be said if these fingerings were tried on a European 'diatonic' recorder.
The modern-tuned, 'contemporary' Native American flute is crafted by many flute makers, so they are readily available. Actually, there are more flute makers at the beginning of this new century, than all of the last century. In 1996, R. Carlos Nakai and James Demars published 'The Art of the Native American Flute' (Amazon.com) which contained a detailed description of 'Nakai Tablature'. Since then, it has become the de facto standard for 'contemporary' Native American flutes. Many songbooks have been published with this system, which Flutree.com provides a catalog. Many of the recent songbooks also include finger guides underneath each note annotated in 'Nakai Tablature'. From the publishers of such books, the most popular songbooks include both finger guides and 'Nakai Tablature'. Also popular are songbooks that include a recording of their melodies.
If you have just begun with Native American flutes, it's advisable to avoid tablature until you are comfortable with your instrument and can improvise your own melodies, as they say, play your heart or the tree tops. And later, if you want to learn the fingering of some old favorite or write down a song that you have just created, then tablature is a good skill to have. Even if you already can read traditional sheet music, its better to playing everyday without Tablature for your first year, than getting into the habit of only playing if sheet music is in front of you and missing the wonderful opportunity for the flute becoming your second voice.
The Flutetree songbook supports both "Nakai Tablature" and finger guides. A couple of drop-down boxes appear in the upper right-hand corner of each song. One allows you to pick the notation used to show the song, such as showing finger guides. The other allows you to chose a flute maker or alternate fingering that may better match your flute. Some songs include lyrics, and you can control if those lyrics are displayed.
Another optional feature of this songbook is a rhythm guide. Underneath the staff a simple notation of '1 / 2 / 3 / 4 /' denotes 'one and two and three and four and'. If you see pairs of slashes '1 / / 2 / / 3 / /', you can read that as 'one and a two and a three and a'. Counting the beats is one way to figure out how long to hold notes and such. Some players don't like to be so rhythmic, because it can get in the way of free expression. For example, listen to the many ways 'Amazing Grace' is sung and played. The quarter notes and half notes are just hints on how to play it. Some players let the lyrics be there guides to how long to hold notes or slur them.
And in this way, all musical notations are inferior to the original performance. They do not show enough detail reproduce great masterpieces. They just hint at them. This is fine, because such perfection would take the heart of the music. So whichever musical shorthand you learn, always remember to put your heart into what you play.
A good place to continue learning about the basic fingering is with the Starter scale. If you can already read sheet music, you may want to jump directly to the primary and extended scale.