Expecting you have the React Native development environment in place:
cd ExampleApp
npm install # make sure you do this inside ExampleApp/
npm start
# In a separate terminal, run:
adb reverse tcp:8081 tcp:8081
react-native run-android
cd ExampleApp
npm install # make sure you do this inside ExampleApp/
# Then:
# 1. Open ExampleApp/ios/ExampleApp.xcodeproj in Xcode
# 2. Click on the run button
Then start clicking the buttons, it should be quite simple.