The slash chords are related to the inverted chords, but with the important difference that the bass note in the slash chord doesn’t belong to the original chord. Let’s clear this out through an example. The chord C/D is a C chord with a D as the base note. This chord, therefore, includes the notes D, C, E and G as opposed to a regular C chord including C, E and G.
Let’s say you’re playing in a band; in this case you probably will stick to the ordinary C chord as the bassist will take care of the bass note D. But playing on your own you should play all the four notes on your guitar. It isn’t strictly necessary in that manner your music will be completely awkward just playing the regular C chord, but you will discover that there’s many possibilities to elaborate a song with slash chords.
Common slash chords
Chord progressions with slash chord
Slash chords are often used to make smooth progressions between chords. Instead of change directly from a C to an Am the slash chord C/B can be put in between. This works well because the note B is flanked by A and C in a musical scale. Try out the progression:
C – C/B – Am
Another example is to insert a G/F# chord between G and Em. F# (F sharp) is positioned between G and E in the scale of G major. The chord progression is therefore as follow:
G – G/F# – Em
A third example is the nice alternative for E - D - A:
E – E/D# – A
Another example making use of Bm/A:
D – Bm/A – G
As an alternative to the ordinary Am to G sequence we can get another feeling by playing:
Am – Am/F# – G
A slight nuance could Em/D placed between Em (possibly with the alternate fingerings XX2000) and C generate:
Em – Em/D – C
The five examples of progressions are all involving smooth movements. It's not always that shifting to another chord via a slash chord works that well. Sometimes there are no perfect changes. Like C/D# ... this should be nice between C and D but there is no chord shape that makes the transition smooth and the bigger changes in finger positions, the less likely there is for the progression to sound great.
By using more of the slash chords in the diagrams above you may find other progressions that also work.