First things first, head over to the Firebase website and either sign in or create a new account. Once you're in, let's get that new Firebase project rolling:

• Hit the "Go to Console" button up in the top right corner.
• Click on the "Add project" button in the Firebase console.
• Give your project a name and pick your country or region.
• Agree to the Firebase Terms of use and then click on the "Create project" button.
• Hang tight for a few seconds, then click "Continue" when your project is ready.

Now, let's connect your Firebase project to your single-page app:

• In the Firebase console, click on the "Add app" button and choose "web".
• Give your app a nickname.
• Copy the auto-generated code snippet to your clipboard.

You'll need to paste this code snippet into your SPA's HTML files (make sure it's on every HTML page). This snippet is what links your app with Firebase, allowing you to use Firebase APIs.

Time to set up Firebase authentication. Follow these steps:

• In your Firebase project console, on the left sidebar, click on "Authentication".
• Go to the "Sign-in method" tab.
• You'll see a list of authentication providers. Enable the ones you want by clicking on the provider, toggling the "Enable" switch, and then clicking "Save". Don't forget to add the authorized domains where you want to authenticate.

With Firebase Authentication set up in the console, you can now use the Firebase Authentication APIs in your single-page app's code:

• First, get a reference to the Firebase Auth instance. In JavaScript, you can do this with firebase.auth().
• Depending on the sign-in method you chose, the commands will differ. For instance, for Google Sign-In, you can use the signInWithPopup function on the auth instance:

const provider = new firebase.auth.GoogleAuthProvider(); 
firebase.auth().signInWithPopup(provider).then((result) => { //User signed in }).catch((error) => { //handle error });

Always handle the promise returned by these functions, as they deal with network requests.

Firebase Auth also offers ways to keep a user’s session active between page reloads and even browser restarts:

• By default, Firebase sessions are persistent, so you don't need to do anything special to make sign-ins last across page reloads.
• You can detect the current user by using firebase.auth().onAuthStateChanged, which gives you a function that gets called whenever the user state changes.

Lastly, make sure to handle errors properly in case of a failed sign-in attempt with the catch block. The error object will give you details on what went wrong.