That website has a good example of how to connect to multiple types of TON wallets, unfortunately the frontend is not open source!

By login, I assume you mean connecting to the site, not necessarily having a backend account system like you would in Web2. That is a different question that can be answered in a different way.

What you're looking for is likely TON Connect! They provide ways to connect wallets to a frontend through their SDK. You can connect with one of their SDK packages:

import TonConnectUI from '@tonconnect/ui'

const tonConnectUI = new TonConnectUI({
    manifestUrl: 'https://<YOUR_APP_URL>/tonconnect-manifest.json',
    buttonRootId: '<YOUR_CONNECT_BUTTON_ANCHOR_ID>'
});

// Try to connect here
const connectedWallet = await tonConnectUI.connectWallet();

Learn more about how to use them with their SDK and documentation.