How to Turn Wi-Fi on / off on Android?

You can use the WifiManager class for this, in particular the function setWifiEnabled . Example (within an activity):

WifiManager wifi = (WifiManager)this.getSystemService(Context.WIFI_SERVICE)
wifi.setWifiEnabled(true); // Liga o WiFi
if (wifi.isWifiEnabled()) {
    // WiFi está ligado
}

Note that you will need to add some permissions:

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

In your particular case, I suggest not turning off WiFi when exiting the app if it was already turned on when the app was opened. In other words, just turn it off if you called yourself.