To create a maj7 chord you have to add a major 7th to a major chord, e.g. a B for a C major chord. Instead of going up seven steps in the major scale you can count back a half step: C → B
Maj7 vs. V7
In a 7th chord (strictly speaking a "dominant 7th" chord or a "V7" chord) we add a 7th to major chord, e.g. a Bb for a C major chord. More about dominant 7th chords here.
There are several common ways of writing a maj7 chord: maj7, Δ7, j7 and ma7 (or MA7)
C → Cmaj7
Taking the "classic" C major chord shape we can lower the C on the B string by one half step.
Drag the slider under the chord shape to the right to change the C into a Cmaj7 that way. Also, check out the whole thing with displayed intervals and tones and watch carefully how the chord is changing.
For all other maj7 chords with the root on A string we can slide the chord shape to the left or right as a whole, e.g. down to Bmaj, Bbmaj7 and finally Amaj7 or up to Dbmaj7, etc.
That's how the whole thing looks when we take the C major barre chord on the 3rd fret: we're replacing the root tone C on the G string with the major seven B.
G → Gmaj7
To add a maj7 to the open G major chord we can lower the root tone on the high E string by one fret.
But somehow it sounds clearer when we leave out the 3rd on A string. The 3rd is present again one octave higher on B string.
Although the interval between the lowest two strings is a 5th when we take the G barre chord, we are dampening the A string like before when we change it into a Gmaj7.
The high E string can also be left out in the Gmaj7 - if not, we have to lay our first finger a bit angular on the fretboard to let a second maj7 ring (like shown here).
Again we can slide the whole grip to the left or right, e.g. to play a Fmaj7 or an Abmaj7, etc.