I have read this before and I have downloaded the BitCoin client, so how do I identify my private key here? I also noticed with my wallet, I only have one bitcoin address, how do I have so many more on CoinBase?
You can export your private key in the debug console, however, don't do that. It is intentionally made difficult to do so that people don't do it and compromise their security.
You can get more addresses by clicking the "new" button in File > Receiving Addresses.