Dominant 7th chords
D → D7
Change a D major into a D7 like this...
Also this grip can be moved like a barre chord to get other V7 chords with the root on the D string, e.g. a Eb7.
Why is a 7th chord called dominant 7th chord or V7 chord?
When we build up stacks of thirds over every note of a major scale (using only notes of the scale), we obtain the modal chords of the major scale. Depending on how much thirds we stack, we'll get triads or seventh chord (or even ninth chords, etc.).
A major chord with a seventh (not a major 7th) is only present on the 5th (V.) scale degree - the so called dominant. That's why this chord is called a dominant seventh chord or V7 chord.
However, in certain harmonical contexts we'll often find V7 chords on other scale degrees as well, without changing the main key.
Further chord shapes
There are quite a few different chord shapes for dominant 7th chords. The root does not always have to be the lowest note, for instance if you've got a second instrument (bass, piano,...) playing the bass note, or if you're packing more than one chord shape of the same chord into a bar to make your accompaniment more interesting.
This lesson is not intended for showing all possibilities. The construction of dominant seventh chords should be clear by now. The chord finder shows more V7 chord shapes - fiddling out others by yourself is of course strictly allowed!