For an immediate look at how some of these sounds work in real life, check out Example 1 (below), which includes both an A7 and an Amaj7. The Beatles used this in the first four bars of the chord progression to the song "Something."

Example 1

From here, it's not so hard to start constructing these chords on other roots. For example, to create a Dmaj7, lower the D on the second string one fret and play the top three strings with one second-fret barre. To play an Em7, start with an E-minor voicing and lower the root on the fourth string two frets to the minor seventh. Since that note is the open D, you can play the resulting chord with just one finger.

Going from D to Dmaj7
Going from Em to Em7

With these new chords in hand, try strumming the first three bars of Erroll Garner's jazz standard "Misty" in the key of A.

Example 2