For Key Signatures, say it says sharp in the f column next to the treble staff but it doesn't have any f notes in that column so do you just not play any sharps or what?
Yep that's right!
A piece should always have a key signature (the sharps or flats grouped in the beginning of the staff). But it could happen that a piece like yours, written in G major (or the relative minor E minor), actually have no F's (the note that should be "sharp" if present).
So you may be playing in the key of G major/E minor, but using (in this case) only white keys! :)
If you're interested in learning more about key signatures, check out these pages: