Chords "with a slash"

We've all seen chords like these: F/C, G/C, C/E.  A song I want to play has no SMN given, only the chords & those appear in it.  I believe it means the voicing of the chord changes.  The song is clearly written in C & I'll probably complicate matters by playing it on my baritone in A <sigh!> requiring further transposing, but first I need to know what to do with the way it's written.  Yes, I know that's for guitar, but I never really understood those slash-type chords there either.