Claim your BTG from your Ledger Nano S hardware wallet with this quick tutorial and some tips on what to do with it.
Video tutorial on d.tube - sorry there are two videos there. It looks like you can post formats that don't work, but you can never delete. This one should work.
Also be aware that currently the BTG network has grinded to a halt so be patient if you're trying to push a transaction through. Good luck!