App.js

import {
  StackNavigator,
} from 'react-navigation';

import Login from './Login';
import Register from './Register';

const App = StackNavigator({
  Login: { screen: Login },
  Register: { screen: Register },
});

export default App;

index.js

import { AppRegistry } from 'react-native';
import App from './App';

AppRegistry.registerComponent('someapp', () => App);

Login.js

import React, { Component } from 'react';
import {
  AppRegistry,
  StyleSheet,
  Text,
  View,
  TouchableHighlight,
} from 'react-native';

export default class Login extends React.Component {
  static navigationOptions = {
    title: 'Login',
  };

  linker(){
    this.props.navigation.navigate("Register");
  }

  render() {
    const { navigate } = this.props.navigation;
    return (
      <View> 
        <TouchableHighlight onPress={this.linker.bind(this)}>
          <Text> Login page </Text>
        </TouchableHighlight>
      </View>
    );
  }
}

Register.js

import React, { Component } from 'react';
import {
  AppRegistry,
  StyleSheet,
  Text,
  View
} from 'react-native';

export default class Register extends React.Component {
  static navigationOptions = {
    title: 'Register',
  };
  render() {
    const { navigate } = this.props.navigation;
    return (
      <View> 
        <Text> Register page </Text>
      </View>
    );
  }
}