How do you use slash chords?
The normal way of notating an inverted chord is to use a “slash”, with the chord name first, then a slash, then the altered bass note. So the inversions described above would be A/C# and A/E. The A/C# gives direction to your progression by giving direction to the bass line.
What does a chord with a slash mean?
In music, especially modern popular music, a slash chord or slashed chord, also compound chord, is a chord whose bass note or inversion is indicated by the addition of a slash and the letter of the bass note after the root note letter. It does not indicate "or". ... Some chords may not otherwise be notated, such as A♭/A.
Is a slash chord just an inversion?
Typically, yes: a slash chord is just an alternative way of notating an inversion. C/G, as you said, means "a C-major chord with G in the bass," which is exactly the same as a C-major chord in second inversion. But not all slash chords are understood as inversions.