How do they load a url inside a webview instead of androids internal browser?

Add this line before the loadUrl() call

bookingView.setWebViewClient(new WebViewClient());

This is the answer:

Features

1. Load a URL on WebView
2. Open another page in the website on Webview dont on local Browser.
3. If you press on backbutton will go to the before page dont out of app.

MainActivity.java

public class MainActivity extends AppCompatActivity {

        WebView webview;
        @Override
        protected void onCreate(Bundle savedInstanceState) {
            super.onCreate(savedInstanceState);
            setContentView(R.layout.activity_main);
            webview = (WebView)findViewById(R.id.webview);
            webView();
        }

    //Metodo llamar el webview
    private void webView(){
        //Habilitar JavaScript (Videos youtube)
        webview.getSettings().setJavaScriptEnabled(true);

        //Handling Page Navigation
        webview.setWebViewClient(new MyWebViewClient());

        //Load a URL on WebView
        webview.loadUrl("http://stackoverflow.com/");
    }

    // Metodo Navigating web page history
    @Override public void onBackPressed() {
        if(webview.canGoBack()) {
            webview.goBack();
        } else {
            super.onBackPressed();
        }
    }

    // Subclase WebViewClient() para Handling Page Navigation
    private class MyWebViewClient extends WebViewClient {
        @Override
        public boolean shouldOverrideUrlLoading(WebView view, String url) {
            if (Uri.parse(url).getHost().equals("stackoverflow.com")) { //Force to open the url in WEBVIEW
                return false;
            }
            Intent intent = new Intent(Intent.ACTION_VIEW, Uri.parse(url));
            startActivity(intent);
            return true;
        }
    }

}

activity_main.xml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical" >

    <WebView android:id="@+id/webview"
        android:layout_width="match_parent"
        android:layout_height="match_parent" />

</LinearLayout>

Include this in AndroidManifest.xml

<uses-permission android:name="android.permission.INTERNET" />

AndroidManifest.xml

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.example.webview" >

    <uses-permission android:name="android.permission.INTERNET" />

    <application
        android:allowBackup="true"
        android:icon="@mipmap/ic_launcher"
        android:label="@string/app_name"
        android:theme="@style/AppTheme" >
        <activity
            android:name=".MainActivity"
            android:label="@string/app_name" >
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
    </application>

</manifest>

RESULT

START PAGE

ANOTHER PAGE IN THE WEBSITE ON WEBVIEW