Quote from: kevinnem on May 06, 2013, 04:59:16 PM

what key I share with others to get paid,

You give a Bitcoin Address from the "Receive Coins" tab to get paid.

Quote from: kevinnem on May 06, 2013, 04:59:16 PM

and what key I use to pay others..

Others will send/tell you one of their bitcoin addresses for you to pay them. You will enter that address in the "Pay To:" field under the "Send Coins" tab.

Quote from: kevinnem on May 06, 2013, 04:59:16 PM

can someone please explain in some detail the "public/private " keys situation, and what I need to back up in order to get my coins back if I lose my computer

The "private keys" are stored in the wallet.dat file that you can backup from the "File" menu.

Generally, you will not know what these private keys are, and you will not use them directly. The Wallet software takes care of using them as needed when creating a transaction.