I know how to create a paper wallet and send bitcoin to it from Coinbase. If I want to spend the paper wallet bitcoin do I just give the merchant my public key? How does the network know I hold the private key from just that private key info? If I want to send the bitcoin to someone do I have to download the entire bitcoin protocol to do that? Is there a smaller version I can use to just send bitcoin? Thanks for your help.
Paper wallets are used for storage only. If you want to spend the bitcoins, you can import the private key from the paper wallet into a wallet on your phone or computer.
I suggest installing Airbitz on your phone and using the "Scan QR Code" feature. It only takes a minute.