I'm trying to play a song, and one of the chords is G/F. I tried to look it up on this site, but it's only showing G/F#, not G/F. So is G/F a typo? Why is it not listed on this site?
G/F means "G-chord with an F in the bass". But technically, this isn't a G-chord at all, because G-chords don't have an F in them. They do, however, have an F#. G-chords with an F rather than an F# are actually G7 chords, not G chords.
More generally: When you see a chord notated, like "G" or "Am" or something, the assumption is either that you'll play the the root of the chord in the bass, or that it doesn't matter if you play an inversion. If the songwriter specifically wants you to play some other particular chord tone in the bass, s/he will write "chord name/some other note", like "G/F" or "Am/E". Such chords are called "inversions".
So a G/F# is a G-chord, but specifically an inversion of a G-chord with the F# in the bass. Since a G-chord with an F in it is actually a G7 chord, you might have more luck looking for G7/F. Or you could just roll your own by taking a G-chord and moving the bass note down two frets.
This webpage shows a guitar tab for G/F as
Or, for those who don't read guitar tabs:
X:0 T:G/F chord T:close position K:none L:1/4 M:none [FGBd]4
X:0 T:G/F chord T:open position (one possibility) K:none L:1/4 M:none [V:V1] [GB]4 [V:V2 clef=bass] [F,D]4
The same page also includes context: G | G/F | C
In that case, the G/F is operating as a G7, as @AlexBasson explained in his answer.
You also might see: G | G/F | C/E
That way, the bass note moves down step-wise from G to E.
...Which brings up another likely context -- step-wise bass motion.
G | G/F | Em7
G | G/F | Edim | Eb7 | D
In any of these cases, you can debate with your music-theory-nerd friends about whether the G/F is really a G7 chord, or whether it's really a G triad with an F passing tone underneath.