The notes of A9 are A, C#, E, G and B. A is the root, C# the major third, E the fifth, G the minor seventh and B the ninth. Said aloud, its notes are A, C sharp, E, G and B.
String by string, low to high, it plays A, E, B, C# and G. It runs from A on string 5 up to G on string 1.
In A9, only one string rings open, string 5, which gives A. String 6 is not played. Your hand covers three frets, from 2 to 4. There is one more position, starting at fret 5.
Change only string 1 in A9 and you have Aadd9. Inside A9 sits a complete Em chord, made of E, G and B. Moving to A, you keep one finger down.
A9 belongs to only one key, D major, where it is the V9.