I am new to the paper wallet, and have a few questions about how to use it. Concretely， I am following the instructions here (https://walletgenerator.net/) to generate a paper wallet for BTC, but I am wondering 1. How can I transfer BTC back and forth between my paper wallet and the GDAX exchange, and 2. Is there any fee to do such transfer? Thanks!
Paper wallets are often a very secure way of storing bitcoins for the long-term but not for two-way transactions.
You can easily transfer bitcoins into your paper wallet from GDAX by going to WITHDRAW FUNDS and putting in the public address part of the paper wallet.
Sending bitcoins to GDAX from a paper wallet is more complicated. You will need to import your private key into a real client.
Once you imported the private key into your client wallet it will allow you to spend your bitcoin and send it to the address provided on GDAX.
Current fees for bitcoin transaction can be found on miningfees.com
Exodus also allows gives you the added option to convert to other crypto-currencies. It works like a currency exchange, using Shapeshift.
Just be mindful that not all desktop wallet clients are created equal. You'd probably be fine using Exodus but often, you sacrifice security for convenience. Make sure you are using a decent antivirus program for your PC and that ought to be sufficient. But I would not keep very large balances on a desktop wallet for an extended period of time.
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.