First things first, let's get a project going in the Firebase Console.

1. Head over to the Firebase Console (https://console.firebase.google.com/).
2. Click "Add Project" and just follow the steps to create a new project.
3. Once your project is up and running, go to "Project Settings."
4. Under "Cloud Messaging," jot down the Server key and Sender ID. You'll need these later.

Time to integrate Firebase into your WeWeb app.

1. Go back to the Firebase Console Project Settings.
2. Under the "General" tab, scroll down to "Your apps" and click the web icon (</>) to create a new web app.
3. Register your app and follow the steps. You'll get a Firebase config object.
4. Copy that Firebase configuration object.

In your WeWeb project:

1. Go to the settings page.
2. Navigate to "Integrations" and find Firebase.
3. Add a new Firebase integration and paste the configuration object you copied earlier.

You might need to add some Firebase libraries to your project.

1. Open your project and go to the dependencies or libraries section.
2. Add these Firebase SDKs:
   ```html ```

Make sure the Firebase Initialization script is in your HTML:

<script>
  var firebaseConfig = {
    apiKey: "YOUR_API_KEY",
    authDomain: "YOUR_PROJECT_ID.firebaseapp.com",
    projectId: "YOUR_PROJECT_ID",
    storageBucket: "YOUR_PROJECT_ID.appspot.com",
    messagingSenderId: "YOUR_SENDER_ID",
    appId: "YOUR_APP_ID",
    measurementId: "YOUR_MEASUREMENT_ID"
  };
  firebase.initializeApp(firebaseConfig);
</script>

Let's ask users to allow notifications.

1. Add a JavaScript function to request permission:
   ```javascript
   const messaging = firebase.messaging();

   function requestPermission() {
   messaging.requestPermission()
   .then(() => {
   return messaging.getToken();
   })
   .then((token) => {
   console.log("FCM Token:", token);
   // Send the token to your server to save it
   })
   .catch((err) => {
   console.error("Permission denied", err);
   });
   }
   ```

2. Call this function when your app initializes.

Set up how to handle incoming messages when users are on your site.

messaging.onMessage((payload) => {
  console.log("Message received. ", payload);
  // Customize the notification appearance
  const notificationTitle = payload.notification.title;
  const notificationOptions = {
    body: payload.notification.body,
    icon: payload.notification.icon,
  };

  var notification = new Notification(notificationTitle, notificationOptions);
});

Send notifications to your Firebase Cloud Messaging tokens.

1. Use the saved FCM tokens to send messages from your server. Here's an example using Node.js and Firebase Admin SDK:
   ```javascript
   const admin = require("firebase-admin");
   const serviceAccount = require("path/to/serviceAccountKey.json");

   admin.initializeApp({
   credential: admin.credential.cert(serviceAccount)
   });

   const message = {
   notification: {
   title: 'Hello World',
   body: 'This is a push notification!'
   },
   token: 'USER_FCM_TOKEN' // Replace with the user's FCM token
   };

   admin.messaging().send(message)
   .then((response) => {
   console.log('Successfully sent message:', response);
   })
   .catch((error) => {
   console.log('Error sending message:', error);
   });
   ```

Make sure everything's working correctly.

1. Deploy your WeWeb application to a live environment.
2. Ensure your app requests notification permissions and saves FCM tokens.
3. Send a test notification from your server and check if it shows up on your web app.

Note: Test on different devices and browsers to make sure everything's compatible.