The slash chords are named so beacuse of the slash symbol in the chord name. For exemple C/D is a C chord with a D as the bass note. This chord, therefore, includes the notes D, C, E and G as opposed to a regular C chord including C, E and G.
The slash chords are related to the inverted chords, but includes also chords in which the bass note doesn’t belong to the original chord.
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.
Overview of slash chords
Additional slash chords
The pictures above show some of the most useful chords with alternative bass notes. However, there is more, and some will be listed here in annotated form:
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
As an alternative to the ordinary Am to G sequence we can get another feeling by playing:
Am – Am/G – G
Another example making use of Bm/A:
D – Bm/A – G
A slight nuance could Em/D placed between Em (possibly with the alternate fingerings XX2000) and C generate:
Em – Em/D – C
Without being very common F/E could be use as an in-between chord by the same principles as the sequences above. (Instead for F - F/E it is also possible and quite easier to play Fmaj7 - Fma7/E.)
F – F/E – Dm
In the same fashion as some of the exemples above, here is one sequence you can use in the key of A.
A – A/G – A/F# – E
The 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.