I have 1/2 Bitcoin on a paper wallet, made before the fork.
My understanding is that now, after the fork, I have 1/2 Bitcoin
and 1/2 Bitcoin Cash. How can I get those (Both BTC and BCC)
from my paper wallet to an exchange to get USD for them. I have
an account at COINBASE but they don't support BCC.
It doesn't mean that when you have your bitcoins on a paper wallet you will automatically get your Bitcoin Cash. I am storing my bitcoins to my Electrum wallet before the fork. What I did to get my own BCC is download an application called Electron Cash (by the way I am only using my Android Phone) installed it, I created a new wallet and then copied my Bitcoin's public key. After that it just synchronized and viola! I have my BCCs the same number as my Bitcoins on my Electrum wallet.