I have read that in order for you to claim bitcoin gold, you must store your bitcoin on a wallet where you have full control of your private keys, for example exodus, electrum or even armory. You will have to export your bitcoin private keys and import them on a wallet that support bitcoin gold, you will then have equivalent bitcoin gold for the amount of bitcoin you had.

I am not yet sure as to which exchanges will support bitcoin gold, but bittrex will probably be one of those exchanges, since currently investors are unable to withdraw or deposit bitcoin on their bittrex wallets.