I hope you already have installed or set up an android studio, emulator, or expo in your machine, I will go through the coding part.

First of all open your command then install the react-native

npx react-native init AwesomeProject

now run your project with the command react-native run-android (if IOS then react-native run-ios)

know more details from here

now you have all the important files, find the App.js file and remove all code from here

import React, {useState} from 'react';
import { StyleSheet, Text, View, Button, TextInput, ScrollView } from 'react-native';

add those two lines in the App.js file

Then I just adding all code after that I will explain step by step:

import React, {useState} from 'react';
import {
  StyleSheet,
  Text,
  View,
  Button,
  TextInput,
  ScrollView,
} from 'react-native';

const App = () => {
  const [enterGoal, setEnterGoal] = useState('');
  const [courseGoals, setCourseGoals] = useState([]);

  const goalInputHandler = enteredText => {
    setEnterGoal(enteredText);
  };

  const addGoalHandler = () => {
    setCourseGoals(currentGoals => [...currentGoals, enterGoal]);
    // setEnterGoal('');
  };

  return (
    <View style={styles.screen}>
      <View style={styles.inputcontainer}>
        <TextInput
          style={styles.input}
          placeholder="Course Goal"
          onChangeText={goalInputHandler}
          value={enterGoal}
        />
        <Button title="ADD" onPress={addGoalHandler} />
      </View>
      <ScrollView>
        {courseGoals.map(goal => (
          <Text style={styles.listItem} key={goal}>
            {goal}
          </Text>
        ))}
      </ScrollView>
    </View>
  );
};

const styles = StyleSheet.create({
  screen: {
    padding: 50,
  },
  inputcontainer: {
    flexDirection: 'row',
    justifyContent: 'space-between',
    alignItems: 'center',
  },
  input: {
    borderColor: 'black',
    borderWidth: 1,
    padding: 10,
    width: '80%',
  },
  listItem: {
    padding: 10,
    backgroundColor: '#ccc',
    borderColor: 'black',
    borderWidth: 1,
    marginVertical: 10,
  },
});

export default App;

I have added a TextInput which is imported from react-native for user input, here is styles.input for a simple design with CSS

  <TextInput
          style={styles.input}
          placeholder="Course Goal"
          onChangeText={goalInputHandler}
          value={enterGoal}
        />

setEnterGoal will store data from the value={enterGoal}

 <Button title="ADD" onPress={addGoalHandler} />

If the user will press on the ADD button then fire addGoalHandler function which will contain

  const addGoalHandler = () => {
    setCourseGoals(currentGoals => [...currentGoals, enterGoal]);
    // setEnterGoal('');
  };

If you use setEnterGoal('') then after every ADD input fill will clear

Now we have all data inside courseGoals

So, now we can mapping those data using,

 <ScrollView>
        {courseGoals.map(goal => (
          <Text style={styles.listItem} key={goal}>
            {goal}
          </Text>
        ))}
      </ScrollView>

I have used ScrollView from react-native for scrolling

here is the final output.

here is the full source code