By clicking on "Unlock Wallet", you'll be greeted with the choice of your wallet provider. WalletConnect will always be available, alongside any wallet providers you have installed on your browser (injected providers).
Choose a wallet provider
Once you've connected with your wallet provider, you can see your v1 and v2 token balance. To swap tokens, you must first hit "Approve", so that the contract has the required allowance to make the transaction.
Hit Approve to have an allowance
This will prompt a confirmation screen with your wallet provider, which once approved, will take a few seconds to load and confirm the block. The "Swap" button should become available then.
Hit Swap to swap your tokens
Once again, "Swap" will prompt a confirmation screen with the wallet provider. Once everything is complete, you should be left with all your v1 tokens now swapped to v2.