Our first 9th chord to study is the major 9th. It always makes sense to start with major as you are never altering the scale, just picking notes from it instead. This makes the scale formulas easy to remember and sets us up for the more difficult formulas.
Whenever you are studying major type chords, the chord construction is pretty simple. In the case of a major 9th chord you simply take your major triad (1st, 3rd, 5th) add the 7th, and then the 9th. It is the addition of the 9th that changes the vibe of the chord to an even more relaxed sounding chord. Here is the formula applied to C major:
To put this into practice on the guitar, below is two common Cmaj9 chord shapes. Notice the notes you are playing and try to call each one out in theoretical terms (i.e. the 1st, 5th etc...). Also notice that we don't necessarily include the 5th in the chord, that is something we will explain fully later on.