App.js

import React from 'react';
import { StyleSheet} from 'react-native';
import { createAppContainer, createStackNavigator } from 'react-navigation'
import HomeScreen from './HomeScreen'
import DetailsScreen from './DetailsScreen'
import EditScreen from './EditScreen'

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

const styles = StyleSheet.create({
  view:{
    flex: 1, 
    alignItems: 'center', 
    justifyContent: 'center',
    margin:10

  },
  button: {
      margin: 20,
      padding: 10,
      backgroundColor: 'wheat'
  }
});


const RootStack = createStackNavigator(
  {
    Home: {
      screen: HomeScreen,
    },
    Details: {
      screen: DetailsScreen,
    },
    Edit: {
      screen: EditScreen,
    },
  },
  {
    initialRouteName: 'Home',
  }
);

const AppContainer = createAppContainer(RootStack);

HomeScreen.js

import React from 'react';
import { View, Text, TouchableOpacity , StyleSheet, FlatList , AsyncStorage} from 'react-native';
import { createAppContainer, createStackNavigator } from 'react-navigation'; // Version can be specified in package.json
import { Button  } from 'react-native-elements';
import Icon from 'react-native-vector-icons/Ionicons';


export default class HomeScreen extends React.Component {

    constructor(props) {
    }

  
   /**
   * render
   *
   */
    render() {
  
  
      return (
        <View style={styles.view}>
          <Text>Home Screen</Text>

          <Button buttonStyle={styles.button} title="★☆☆" onPress={(e) => this.props.navigation.push('Details',1)}>
          </Button>

          <Button buttonStyle={styles.button} title="★★☆" onPress={(e) => this.props.navigation.push('Details',2)}>
          </Button>

          <Button buttonStyle={styles.button} title="★★★" onPress={(e) => this.props.navigation.push('Details',3)}>
          </Button>

          <Button buttonStyle={styles.button} title="問題編集" onPress={(e) => this.props.navigation.push('Edit')}>
          </Button>

            <Button buttonStyle={styles.button} title="スプレッドシートからロード" onPress={(e) => this.handleGoogleSheet(e)}>
            <Text style={styles.text}></Text>
          </Button>

        </View>
      );
    }
  }

  const styles = StyleSheet.create({
    view:{
      flex: 1, 
      alignItems: 'center', 
      justifyContent: 'center',
      margin:10,
    },
    button: {
        margin: 10,
        padding: 1,
        backgroundColor: 'rgba(0,103,171,1)',
        borderRadius: 5,
        width:300
    },
    text:{
      color: 'white'
    },
    actionButtonIcon: {
      fontSize: 20,
      height: 22,
      color: 'white',
    }
  });

DetailsScreen.js

import React from 'react';
import { Button, View, Text, TouchableOpacity , StyleSheet, FlatList , AsyncStorage} from 'react-native';

const styles = StyleSheet.create({
    view:{
      flex: 1, 
      alignItems: 'center', 
      justifyContent: 'center',
      margin:10
  
    },
    button: {
        margin: 20,
        padding: 10,
        backgroundColor: 'wheat'
    }
  });

export default class DetailsScreen extends React.Component {

    render() {
      console.log(this.props.navigation.state.params)
      return (
        <View style={{ flex: 1, alignItems: 'center', justifyContent: 'center' }}>
          <Text>Details Screen {this.props.navigation.state.params}</Text>
          <Button
            title="Go to Details... again2"
            onPress={() => this.props.navigation.push('Details')}
          />
          <Button
            title="Go to Home"
            onPress={() => this.props.navigation.navigate('Home')}
          />
          <Button
            title="Go back"
            onPress={() => this.props.navigation.goBack()}
          />
        </View>
      );
    }
  }

pushするときの第二引数にセットできる

          <Button buttonStyle={styles.button} title="★☆☆" onPress={(e) => this.props.navigation.push('Details',1)}>
          </Button>

this.props.navigation.state.paramsで取得できる

<Text>Details Screen {this.props.navigation.state.params}</Text>

 this.props.navigation.push('Details',{star:1,rank:2}

のようにすることで、

{this.props.navigation.state.params.star} {this.props.navigation.state.params.rank}

のように取り出すことができる。