The slash chords (a.k.a. split chords) are named so because of the slash symbol in the chord name. For example C/D is a C chord with a D as the bass note. Therefore, it 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 will instead play all the four notes on your guitar. It isn’t strictly necessary in the way that your music will be completely awkward just playing the regular C chord, but you will discover that there’re 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. But there is more, and some are listed here in annotated form:
When the instrument sets the limit
It's possible to play all combinations in the area of chords with alternative bass notes. However, in some cases it doesn't work very well because of the instrument. One example is A/D. The best way to play this is probably by using Drop D tuning, in standard tuning its hard to play in any natural way.
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 as follows:
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
Chord progressions with two slash chords
In the same fashion as some of the examples above, but using two slash chords is also an alternative in some occasions.
Am – Am/G – Am/F# – F
This is a nice sequence and you can to play to strum the block chords or just the bass strings in the Am/G, Am/F# movement, or something in between. The following progression has many similarities:
A – A/G – A/F# – E
For the above sequence you need to play the A chord with only the index fingers or use the thumb for the bass strings.
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#, which on piano had been suitable between C and D, but there is no chord shape on the guitar that makes the transition smooth, and the bigger the changes are in finger positions, the less likely that the progression to sound great.
By using more of the slash chords in the diagrams above you may find other progressions that also work.