First things first, head over to the Firebase console at console.firebase.google.com. If you don't have a Google account yet, you'll need to make one. Once you're in the Firebase console, click on 'Create a project'. Pop in your project name, agree to the Firebase terms, and hit 'Continue'.

After you've got your Firebase project set up, go to your project's settings and click on 'Project settings'. Then, navigate to the 'Cloud Messaging' tab. Here, you'll find your 'Server key' which will come in handy later.

Make sure you have a Supabase account ready to go. If not, just hop over to supabase.io to create a new account and start a new project. You'll find your Supabase URL and API key in your project settings, and you'll need these later.

Now, grab the Firebase server key from Step 2 and the Supabase URL and API key from Step 3 to integrate Firebase Cloud Messaging with Supabase. The exact method will depend on the programming language you're using. Here's an example using JavaScript:

const fetch = require('node-fetch');

// These values are from your Firebase project's Cloud Messaging tab
const firebaseServerKey = 'YOUR_FIREBASE_SERVER_KEY';

// These values are from your Supabase project's settings
const supabaseUrl = 'YOUR_SUPABASE_URL';
const supabaseApiKey = 'YOUR_SUPABASE_API_KEY';
const tableName = 'messages';

// This is where you send a message
async function sendMessageToSupabase(message) {
    const row = {
        message,
        status: 'pending',
    };

    const response = await fetch(`${supabaseUrl}/rest/v1/${tableName}`, {
        method: 'POST',
        headers: {
            'apikey': supabaseApiKey,
            'Content-Type': 'application/json',
        },
        body: JSON.stringify(row),
    });

    if (!response.ok) {
        const error = await response.text();
        throw new Error(`Failed to send message: ${error}`);
    }

    const data = await response.json();
    console.log(`Message sent: ${data}`);
}

Once you've got the integration all set up, it's time to give it a whirl. Send some test messages just like you would in a real-world scenario and see if they're being received and processed correctly.

Keep in mind, every project is a bit different. This guide gives you a general idea, but you might need to tweak things to fit your specific needs.