Sign In and sign up with email and password in Android  Studio with firebase --   

for sign up

Step 1 - in manifest file add permission

<uses-permission android:name="android.permission.INTERNET" />

activity_login.xml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:background="@drawable/text_bg"
    android:gravity="center"
    android:orientation="vertical"
    tools:context=".LogInActivity">

    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:layout_margin="11dp"
        android:gravity="center"
        android:orientation="vertical">

        <EditText
            android:id="@+id/emailAddress"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_marginTop="11dp"
            android:background="@drawable/text_bg"
            android:ems="10"
            android:hint="Email Adress"
            android:inputType="textEmailAddress"
            android:padding="11dp" />

        <EditText
            android:id="@+id/password"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_marginTop="11dp"
            android:background="@drawable/text_bg"
            android:ems="10"
            android:hint="Password"
            android:inputType="textPassword"
            android:padding="11dp" />

        <Button
            android:id="@+id/loginBtn"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_marginTop="11dp"
            android:padding="11dp"
            android:text="Log In" />

        
    </LinearLayout>

</LinearLayout>

Step 2-

initialize before onCreate method

private Button signUpBtn;
private EditText fullName, emailAddress, password;
private FirebaseAuth auth;

Step 3 - Write code in onCreate method

signUpBtn = findViewById(R.id.signUp_Btn);

fullName = findViewById(R.id.fullName);
emailAddress = findViewById(R.id.emailAddress);
password = findViewById(R.id.password);

auth = FirebaseAuth.getInstance();



signUpBtn.setOnClickListener(new View.OnClickListener() {
    @Override
    public void onClick(View v) {

        String name, email, pass;
        name = fullName.getText().toString();
        email = emailAddress.getText().toString();
        pass = password.getText().toString();

        auth.createUserWithEmailAndPassword(email,pass).addOnCompleteListener(new OnCompleteListener<AuthResult>() {
            @Override
            public void onComplete(@NonNull Task<AuthResult> task) {
                if (task.isSuccessful()) {
                   
                }else{
                    
                }
            }
        });
    }
});

for sign method-

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:background="@drawable/text_bg"
    android:gravity="center"
    android:orientation="vertical"
    tools:context=".LogInActivity">

    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:layout_margin="11dp"
        android:gravity="center"
        android:orientation="vertical">

        <EditText
            android:id="@+id/fullName"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_marginTop="11dp"
            android:padding="11dp"
            android:background="@drawable/text_bg"
            android:ems="10"
            android:hint="Full Name"
            android:inputType="textPersonName" />

        <EditText
            android:id="@+id/emailAddress"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_marginTop="11dp"
            android:background="@drawable/text_bg"
            android:ems="10"
            android:hint="Email Address"
            android:inputType="textEmailAddress"
            android:padding="11dp" />

        <EditText
            android:id="@+id/password"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_marginTop="11dp"
            android:background="@drawable/text_bg"
            android:ems="10"
            android:hint="Password"
            android:inputType="textPassword"
            android:padding="11dp" />

        <Button
            android:id="@+id/loginBtn"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:layout_marginTop="11dp"
            android:padding="11dp"
            android:text="Sign Up" />

        4
    </LinearLayout>

</LinearLayout>

private Button logInBtn;
private EditText emailAddress, password;
private FirebaseAuth auth;

    logInBtn = findViewById(R.id.loginBtn);
    emailAddress = findViewById(R.id.emailAddress);
    password = findViewById(R.id.password);
    auth = FirebaseAuth.getInstance();


  
    logInBtn.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            String email, pass;
            email = emailAddress.getText().toString();
            pass = password.getText().toString();
            auth.signInWithEmailAndPassword(email,pass).addOnCompleteListener(new OnCompleteListener<AuthResult>() {
                @Override
                public void onComplete(@NonNull Task<AuthResult> task) {
                    if (task.isSuccessful()) {
                        
                    }else {
                        
                    }
                }
            });
        }
    });
}