Add below dependencies to your build.gradle

  // Facebook login
    compile 'com.facebook.android:facebook-android-sdk:4.21.1'

Add below helper class to your utility package:

/**
 * Created by Andy
 * An utility for Facebook
 */
public class FacebookSignInHelper {
    private static final String TAG = FacebookSignInHelper.class.getSimpleName();
    private static FacebookSignInHelper facebookSignInHelper = null;
    private CallbackManager callbackManager;
    private Activity mActivity;
    private static final Collection<String> PERMISSION_LOGIN = (Collection<String>) Arrays.asList("public_profile", "user_friends","email");
    private FacebookCallback<LoginResult> loginCallback;



    public static FacebookSignInHelper newInstance(Activity context) {
        if (facebookSignInHelper == null)
            facebookSignInHelper = new FacebookSignInHelper(context);
        return facebookSignInHelper;
    }


    public FacebookSignInHelper(Activity mActivity) {
        try {
            this.mActivity = mActivity;
            // Initialize the SDK before executing any other operations,
            // especially, if you're using Facebook UI elements.
            FacebookSdk.sdkInitialize(this.mActivity);
            callbackManager = CallbackManager.Factory.create();
            loginCallback = new FacebookCallback<LoginResult>() {
                @Override
                public void onSuccess(LoginResult loginResult) {
                   // You are logged into Facebook
                }

                @Override
                public void onCancel() {
                    Log.d(TAG, "Facebook: Cancelled by user");
                }

                @Override
                public void onError(FacebookException error) {
                    Log.d(TAG, "FacebookException: " + error.getMessage());
                }
            };
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    /**
     * To login user on facebook without default Facebook button
     */
    public void loginUser() {
        try {
            LoginManager.getInstance().registerCallback(callbackManager, loginCallback);
            LoginManager.getInstance().logInWithReadPermissions(this.mActivity, PERMISSION_LOGIN);
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
    

    /**
     * To log out user from facebook
     */
    public void signOut() {
        // Facebook sign out
        LoginManager.getInstance().logOut();
    }

    public CallbackManager getCallbackManager() {
        return callbackManager;
    }

    public FacebookCallback<LoginResult> getLoginCallback() {
        return loginCallback;
    }

    /**
     * Attempts to log debug key hash for facebook
     *
     * @param context : A reference to context
     * @return : A facebook debug key hash
     */
    public static String getKeyHash(Context context) {
        String keyHash = null;
        try {
            PackageInfo info = context.getPackageManager().getPackageInfo(
                    context.getPackageName(),
                    PackageManager.GET_SIGNATURES);
            for (Signature signature : info.signatures) {
                MessageDigest md = MessageDigest.getInstance("SHA");
                md.update(signature.toByteArray());
                keyHash = Base64.encodeToString(md.digest(), Base64.DEFAULT);
                Log.d(TAG, "KeyHash:" + keyHash);
            }
        } catch (PackageManager.NameNotFoundException e) {
            e.printStackTrace();
        } catch (NoSuchAlgorithmException e) {
            e.printStackTrace();
        } catch (Exception e) {
            e.printStackTrace();
        }
        return keyHash;
    }
}

Add below code in Your Activity:

FacebookSignInHelper facebookSignInHelper = FacebookSignInHelper.newInstance(LoginActivity.this, fireBaseAuthHelper);
facebookSignInHelper.loginUser();

Add below code to your OnActivityResult:

 facebookSignInHelper.getCallbackManager().onActivityResult(requestCode, resultCode, data);

If you want to retrieve the details of a user's Facebook profile, you need to set permissions for the same:

loginButton = (LoginButton)findViewById(R.id.login_button);

loginButton.setReadPermissions(Arrays.asList("email", "user_about_me"));

You can keep adding more permissions like friends-list, posts, photos etc. Just pick the right permission and add it the above list.

Note: You don't need to set any explicit permissions for accessing the public profile (first name, last name, id, gender etc).

Once you first add the Facebook login/signup, the button looks something like:

Most of the times, it doesn't match with the design-specs of your app. And here's how you can customize it:

<FrameLayout
    android:layout_below="@+id/no_network_bar"
    android:id="@+id/FrameLayout1"
    android:layout_width="match_parent"
    android:layout_height="wrap_content">

    <com.facebook.login.widget.LoginButton
        android:id="@+id/login_button"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:visibility="gone" />

    <Button
        android:background="#3B5998"
        android:layout_width="match_parent"
        android:layout_height="60dp"
        android:id="@+id/fb"
        android:onClick="onClickFacebookButton"
        android:textAllCaps="false"
        android:text="Sign up with Facebook"
        android:textSize="22sp"
        android:textColor="#ffffff" />
</FrameLayout>

Just wrap the original com.facebook.login.widget.LoginButton into a FrameLayout and make its visibility gone.

Next, add your custom button in the same FrameLayout. I've added some sample specs. You can always make your own drawable background for the facebook button and set it as the background of the button.

The final thing we do is simply convert the click on my custom button to a click on the facecbook button:

//The original Facebook button
LoginButton loginButton = (LoginButton)findViewById(R.id.login_button);

//Our custom Facebook button
fb = (Button) findViewById(R.id.fb);

public void onClickFacebookButton(View view) {
    if (view == fb) {
        loginButton.performClick();
    }
}

Great! Now the button looks something like this:

1. You have to setup the prerequisites.

2. Add the Facebook activity to the AndroidManifest.xml file:

   <activity 
       android:name="com.facebook.FacebookActivity"
       android:configChanges= "keyboard|keyboardHidden|screenLayout|screenSize|orientation"
       android:theme="@android:style/Theme.Translucent.NoTitleBar"
       android:label="@string/app_name" />
   

3. Add the login button to your layout XML file:

   <com.facebook.login.widget.LoginButton
       android:id="@+id/login_button"
       android:layout_width="wrap_content"
       android:layout_height="wrap_content" />   
   

4. Now you have the Facebook button. If the user clicks on it, the Facebook login dialog will come up on top of the app's screen. Here the user can fill in their credentials and press the Log In button. If the credentials are correct, the dialog grants the corresponding permissions and a callback is sent to your original activity containing the button. The following code shows how you can receive that callback:

   loginButton.registerCallback(callbackManager, new FacebookCallback<LoginResult>() {
       @Override
       public void onSuccess(LoginResult loginResult) {
           // Completed without error. You might want to use the retrieved data here.
       }
   
       @Override
       public void onCancel() {
           // The user either cancelled the Facebook login process or didn't authorize the app.
       }
   
       @Override
       public void onError(FacebookException exception) {
           // The dialog was closed with an error. The exception will help you recognize what exactly went wrong.
       }
   });  
   

Facebook SDK 4.0 onwards, this is how we logout:

com.facebook.login.LoginManager.getInstance().logOut();

For versions before 4.0, the logging out is gone by explicitly clearing the access token:

Session session = Session.getActiveSession();
session.closeAndClearTokenInformation();