• Head over to the Supabase website and either sign up or log in.
• Start a new project by giving it a name and picking your preferred database region.
• Once your project is up and running, go to the project dashboard to grab your project's API keys and URL.

• In the Supabase dashboard, navigate to the SQL editor.
• Create tables for users and messages. Here's some example SQL scripts:

create table users (
  id uuid not null primary key,
  username text not null,
  created_at timestamp not null default now()
);

create table messages (
  id uuid not null primary key,
  user_id uuid references users(id),
  content text not null,
  created_at timestamp not null default now()
);

• In the Supabase dashboard, go to the "Database" section and enable the realtime extension.
• Create a policy to let authenticated users use the real-time features:

begin;

-- Create a policy for users
create policy "Allow authenticated read access" on users
  for select using (auth.role() = 'authenticated');

-- Create a policy for messages
create policy "Allow authenticated read access" on messages
  for select using (auth.role() = 'authenticated');

-- Enable for all authenticated users
alter table users enable row level security;
alter table messages enable row level security;

commit;

• Install the Supabase JavaScript client:
  ```bash
  npm install @supabase/supabase-js
  ```

• Initialize Supabase with your project's URL and public API key:

  ```javascript
  import { createClient } from '@supabase/supabase-js';

  const supabaseUrl = 'https://your-project-ref.supabase.co';
  const supabaseKey = 'public-anon-key';
  const supabase = createClient(supabaseUrl, supabaseKey);
  ```

• Use Supabase's authentication to manage user sign-up and login. Here's an example with email and password:

  ```javascript
  // Sign up user
  const { user, error } = await supabase.auth.signUp({
  email: 'example@example.com',
  password: 'password123',
  });

  // Log in user
  const { user, error } = await supabase.auth.signIn({
  email: 'example@example.com',
  password: 'password123',
  });
  ```

• Fetch users:
  ```javascript
  const { data: users, error } = await supabase
  .from('users')
  .select('*');
  ```

• Fetch messages:
  ```javascript
  const { data: messages, error } = await supabase
  .from('messages')
  .select('*')
  .order('created_at', { ascending: true });
  ```

• Insert new messages:
  ```javascript
  const { data, error } = await supabase
  .from('messages')
  .insert([{ user_id: user.id, content: 'Hello, world!' }]);
  ```

• Listen for new messages in real-time:
  ```javascript
  supabase
  .from('messages')
  .on('INSERT', payload => {
  console.log('New message:', payload.new);
  // Update the UI or state with the new message
  })
  .subscribe();
  ```

• Create a frontend interface for displaying messages and a form for sending messages. Here's an example with React:

  ```jsx
  import React, { useState, useEffect } from 'react';

  function ChatApp() {
  const [messages, setMessages] = useState([]);
  const [newMessage, setNewMessage] = useState('');

  useEffect(() => {
  // Fetch existing messages
  fetchMessages();
  // Set up real-time listeners
  setupRealtimeListeners();
  }, []);

  const fetchMessages = async () => {
  const { data } = await supabase
  .from('messages')
  .select('*')
  .order('created_at', { ascending: true });
  setMessages(data);
  };

  const sendMessage = async (e) => {
  e.preventDefault();
  await supabase.from('messages').insert([{ content: newMessage }]);
  setNewMessage('');
  };

  const setupRealtimeListeners = () => {
  supabase
  .from('messages')
  .on('INSERT', payload => {
  setMessages(messages => [...messages, payload.new]);
  })
  .subscribe();
  };

  return (
  

  
  

  
  {messages.map(message => (
  

  {message.content}

  
  ))}
  

  
  

  
  <input
  type="text"
  value={newMessage}
  onChange={(e) => setNewMessage(e.target.value)}
  />
  Send
  

  
  
  
  );
  }
  ```

• Run the app and test the real-time chat functionality.

The above steps will help in creating a basic chat application using Supabase. Further enhancements can include better UI designs, emoji support, file sharing, and more.