When you run your app, it starts a server at your machine, at port 19000 or 19001, to which you will connect using the Expo application, which you can find at https://expo.io/learn, available for both Android or iOS. Install it by following the instructions onscreen:

When you open the Expo app for the first time, it will look like the following screenshot. Note that both the phone and your machine must be in the same local network, and your machine must also allow connections to ports 19000 and 19001; you may have to modify your firewall for this to work:

After you use the Scan QR Code option, there will be some synchronization, and soon you'll get to see your basic code running with no problems:

Furthermore, if you modify the App.js source code, the changes will be immediately reflected in your device, which means all is well! To make sure this happens, shake the phone to enable the debugging menu, and make sure that Live Reload and Hot Reloading are enabled. You'll also require Remote JS Debugging for later. Your phone should look as follows: