The notes of Abadd9 are Ab, C, Eb and Bb. Ab is the root, C the major third, Eb the fifth and Bb the ninth. Said aloud, its notes are A flat, C, E flat and B flat.
From the low string to the high one you hear Ab, Eb, Ab, C, Eb and Bb. Of the six strings you play, two give Ab, the note that names the chord. The lowest note is Ab on string 6 and the highest is Bb on string 1.
You play Abadd9 with a barre at fret 4. Everything fits between frets 4 and 6. The second shape on this page starts at fret 11.
Ab is one change away. String 1 moves from fret 6 to fret 4, bringing in Ab, the root of Ab. It shares two notes with Fm, Ab and C. Going to Eb, two positions stay the same.
You will find Abadd9 in six different keys. In Ab major it is the Iadd9, in Db major the Vadd9 and in Eb major the IVadd9. The rest appear in the key list.