To understand how chords with 7ths work, you need to know the scale you are using. The chords most commonly used are built on thirds, so if you choose a scale and then a note from that scale, you'll see what chords are maj7 chords, by ascending thirds from the note you chose. *
In the major scale, only the I and IV are major chords and have a major 7th.
So, let's say you want to use the Amaj7 chord. One way to look at this chord would be to consider it the Imaj7 from the A major scale. The chord is built on thirds -- A,C#,E,G# (G# is a major 7th). After the Amaj7 chord, you can use any chord from the scale, like you would use if you simply had a A (without the maj7).
Pretty much the same would work if you considered it as a IVmaj7. It would be the IV from the E major scale. So, you can create a chord progression in the E major scale and instead of a simple A chord, to play a nice Amaj7.
What I like to do sometimes is to play the chord as it is, without the 7th and then add the 7th.
Also, I've never seen a Vmaj7 chord. The V usually is dominant (V7); that means it has a minor 7th instead of a major one; one semitone lower.
*The V doesn't have a major seventh. Let's assume we are in the A major scale. The notes in the A major scale are A,B,C#,D,E,F#,G#. The V chord has E as a root. Let's ascend thirds from E and see what kind of chord we have:
- E (root)
- G# (major third)
- B (perfect fifth); so far we have a major chord
- D (minor 7th).
So the V is a 7 chord, not a maj7 one.