Alright, first things first, you need a Firebase project. Head over to the Firebase Console (https://console.firebase.google.com/), click on “Add project,” and just follow the steps. It's pretty straightforward.

Next up, in the Firebase console, hit the “Add App” button. Pick the platform your app is on (iOS, Android, etc.), and follow the prompts to get your app registered. Easy peasy.

Now, go to the project settings and find the “Cloud Messaging” tab. Jot down the server key - you’ll need it later. Then, head over to the “Authentication” page in the Firebase console. Under the “Sign-In Method” tab, enable the “Email/Password” sign-in method.

To get Firebase working in your app, you need to add the Firebase SDK to your project. The steps will vary depending on your app's platform. Just follow the instructions on the console to get the SDK installed.

Firebase lets users sign up with an email and password. You can use the createUserWithEmailAndPassword function for this.

auth.createUserWithEmailAndPassword(email, password)
  .then((userCredential) => {
    var user = userCredential.user;
  })
  .catch((error) => {
    console.error(error);
  });

To log in users who already have an account, use the signInWithEmailAndPassword function.

auth.signInWithEmailAndPassword(email, password)
  .then((userCredential) => {
    var user = userCredential.user;
  })
  .catch((error) => {
    console.error(error);
  });

Firebase takes care of user sessions automatically. After a successful sign-in, Firebase can remember the user using the onAuthStateChanged function. This will also detect when the user's sign-in state changes.

auth.onAuthStateChanged((user) => {
  if (user) {
    console.log(user);
  } else {
    console.log('User is signed out');
  }
});

Signing out a user is super simple with .signOut().

auth.signOut().then(() => {
  console.log('User signed out');
});

And there you have it! Firebase authentication in a nutshell.