Assuming you have already created a paperwallet using the Bitaddress software download, located on Github (pointbiz), you will need to find out if GDAX has a wallet service for its customers.
This wallet would be a wallet you created on GDAX using the exchange's wallet service. Not all exchanges offer a wallet service. I know CEXio doesn't. you will need this address to send bitcoin FROM your paper wallet TO the exchange wallet. So how do you use the private key on a paper wallet, to send funds to the exchange wallet?
Firstly, in order to release funds from your paper wallet, you are going to need to use a thin client (desktop "hot" wallet client) for bitcoin, like Electrum, or Exodus, to name a few. Exodus is the most user-friendly desktop wallet for beginners.
Learn how your chosen desktop wallet works and generates key pairs because you are going to need to either SWEEP you paper wallet's private key in to the desktop wallet or you will need to IMPORT your paper wallet's private key into the desktop wallet. The decision to do one vs the other depends upon how the desktop manages private keys.
To summarize; go to https://www.exodus.io/releases/
download it, it's free! Follow instructions carefully and make sure you are comfortable using the software before importing/sweeping your paper wallet's private keys into Exodus. Once you have done that step you can use exodus to send bitcoin to your exchange address.