How do I receive Bitcoins from my clients who owe me money? I do not have a web site. Currently I send my clients an invoice. They discharge the invoice by sending me a check drawn on their bank checking account. Do I have to send them a Bitcoin "key" or account number of some kind?
You send them a bitcoin address along with the invoice. Use a different address each time, so that you can tell who paid you.
There are do-it-yourself methods (e.g., generate addresses using the bulk mode of BitAddress.org and send those out as payment addresses) but that requires a fair amount of tracking and manual effort.
Coinbase requires control of your bitcoins. You can try other services like blockonomics that allow you to generate P2P invoices. Or you can just directly send the client your bitcoin address/amount through email.