I don't know what shape they're using but F add G means exatly that. You play F (any shape) and if you've any fingers left you add on the nearest G note - but make sure you don't lose an essential chord tone.
Here's a common 4 string one
XX3213. It's just the common 4 string F chord with your pinky on string 1 fret 3.
Doing that means losing the note F on string 1 fret 1 but there's another F on string 4 so it's no loss.
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