These chords are interesting. If you know the major chords, major 7 chords just take out one of the octaves and “flatten” it by one semitone or one fret. Just like all the other chords, muting strings is also key to a clean sound!
The C major chord is a great example because all of the notes in a C major scale are natural (no sharps or flats required). The C major chord (shorthand: X32010) is the following notes on guitar: C E G C E. If you take the “octave” C, the higher C on the 2nd string, and flatten it by one semitone, you get the C major 7 chord (X32000) C E G B E.
I find it very helpful to try and memorize the notes played in each chord. For my benefit, and possibly yours, here are the notes in each of the chords shown below:
Cmaj7 C E G B E
Dmaj7 D A C# F#
Emaj7 E B D# G# B E
Fmaj7 F A C E
Gmaj7 G B D G B D
Amaj7 A E G# C E
Bmaj7 B F# A# D#
