The notes of Gadd9 are G, B, D and A. G is the root, B the major third, D the fifth and A the ninth.
From the low string to the high one you hear G, B, D, A, B and G. The root, G, shows up twice in the main shape. The lowest and highest notes are both G, two octaves apart, on strings 6 and 1.
Gadd9 lets two strings ring open. String 4 gives D and string 2 gives B. Everything fits between frets 2 and 3. Besides the main one there are two more shapes, at frets 2 and 3.
G is one change away. String 3 is left open, bringing in G, the root of G. It shares two notes with Em, G and B. The change that keeps the most fingers still is to Em. One stays in place.
Gadd9 shows up in six keys. In G major it is the Iadd9, in C major the Vadd9 and in D major the IVadd9. The rest appear in the key list.