You need the following permissions in your manifest file:
<uses-permission android:name="android.permission.ACCESS_WIFI_STATE"></uses-permission>
<uses-permission android:name="android.permission.CHANGE_WIFI_STATE"></uses-permission>
Then you can use the following in your activity class:
WifiManager wifiManager = (WifiManager) this.getApplicationContext().getSystemService(Context.WIFI_SERVICE);
wifiManager.setWifiEnabled(true);
wifiManager.setWifiEnabled(false);
Use the following to check if it's enabled or not
boolean wifiEnabled = wifiManager.isWifiEnabled()
You'll find a nice tutorial on the subject on this site.