how do flute fingering charts work?

When you are reading through your music and you do not know a fingering for a note you would look it up. As you look at it it will have filled in spots that represent the fingers that should be down and non filled in spots that represent the fingers that should be up. It should appear in the same direction that you are holding your flute.

At risk of annoying people here by being just too helpful with information:.....

A good fingering chart will show you which fingers to put on which keys of the flute.

If you go to http://www.wfg.woodwind.org/flute/
you can click on which octave you want the notes in, and you will get a fingering code, both using a finger numbering system, and a flute key diagram system. In the finger numbering system, the first "1,2,3" represents your left hand (index, middle and ring fingers) and the second "1,2,3" represents your right hand similarly.

To make these codes clearer, click on "Description of keys and fingering notation" at the top of the opening web page.