react-navigation-v1-push

App.js

class HomeScreen extends React.Component {
  render() {
    return (
      <View style={styles.container}>
        <Text>HomeScreen</Text>
        <Text onPress={() => this.props.navigation.push('Settings')}>Go to Settings</Text>
      </View>
    );
  }
}

class SettingsScreen extends React.Component {
  ...
}

class DetailScreen extends React.Component {
  ...
}

const HomeStack = StackNavigator({ Home: HomeScreen, Detail: DetailScreen });
const AppNavigator = StackNavigator({ HomeStack, Settings: SettingsScreen });

export default class App extends React.Component {
  render() {
    return <AppNavigator />;
  }
}