1. Head over to the Firebase Console.
2. Click on Add project and just follow the steps to get your project up and running.
3. Once you're done, you'll land on the Firebase project dashboard.

1. Go to the Authentication section in the Firebase Console.
2. Click on Get Started.
3. Turn on the sign-in methods you want (like Email/Password).

1. Head to Project Settings.
2. Click on the Service Accounts tab.
3. Hit Generate new private key and download the JSON file. Keep it safe.

1. Make sure Node.js is installed.

2. Open your terminal or command prompt.

   ```bash
   npm install -g firebase-tools
   ```

3. Log in to Firebase.

   ```bash
   firebase login
   ```

4. Initialize Firebase in your project directory.

```bash
firebase init
```

1. Select Functions and pick your Firebase project from the list.

1. Go to the functions directory inside your project.

2. Install Firebase Admin and Functions SDK.

   ```bash
   cd functions
   npm install firebase-admin firebase-functions
   ```

1. Open index.js inside the functions directory.

2. Add this code to trigger an event when a user signs up:

   ```javascript
   const functions = require('firebase-functions');
   const admin = require('firebase-admin');
   admin.initializeApp();

   exports.sendWelcomeEmail = functions.auth.user().onCreate((user) => {
   const email = user.email;
   const displayName = user.displayName;
   
   // Send welcome email using your preferred method such as nodemailer
   // For illustration purposes, just console.log
   console.log(Sending welcome email to ${email} (${displayName}));
   
   // You can integrate any email-sending service here
   // Example (commented out); requires proper mailing setup
   // const mailgun = require('mailgun-js')({apiKey: 'your-api-key', domain: 'your-domain'});
   // const data = {
   // from: 'Your App noreply@yourapp.com',
   // to: email,
   // subject: 'Welcome!',
   // text: Hello ${displayName || ''}, welcome to our app!
   // };
   // return mailgun.messages().send(data);
   
   return null;
   });
   ```

1. Deploy your function to Firebase.

   ```bash
   firebase deploy --only functions
   ```

2. Wait for the deployment to finish. Once it's done, your Cloud Function will be live and ready to trigger on any new user sign-ups.

1. Go back to the Authentication section in the Firebase Console.
2. Create a new user manually or sign up a new user through your app.
3. Check the logs to make sure the welcome email or event is triggered correctly. Head to the Functions section and check the Logs.

That's it! The Firebase Cloud Function is now set up to trigger an event whenever a new user signs up.