Now that the hardware is up-and-running, you can run the examples in the IDE. If you bring up the IDE and select Examples | Wi-Fi, you can see that there are many choices:

The most basic of these choices is the ScanNetworks sketch. If you select this sketch and then open the Serial Monitor Window, you should see something like this:

The other sketches provide further capabilities. There are sketches that show how to connect using WPA or WEP security protocols. One of the most useful is the SimpleWebServer Wi-Fi that shows how to turn an LED on and off over the Wi-Fi network via an external web page. Simply connect a resistor and LED in series between GND and digital IO pin nine, edit the sketch to include the SSID and password of your network, and then open a web browser. When you open the Serial Monitor, it will show you connected to the network:

Now go on the host computer and enter the address shown in the address line. The following should appear on your browser:

You can now turn the LED on and off.