On the login or registration page click Choose Wallet & Register or Choose Wallet & Sign In. Pick your wallet in the picker, for example MetaMask, Rabby or WalletConnect for mobile.

1. The app requests a one-time nonce for your address.
2. You sign a message in your wallet, with no gas fee and no transaction.
3. Once verified, you are logged in, or your wallet is linked to your account.

For details, see the documentation: Connect Wallet and Sign In (SIWE) and Hydra Wallet Login.