WiFi communication PC - Arduino

Hello All
I use an Arduino MEGA 1256 and a WiFi-Shield (AT32UC3A1512).
What other hardware do I need to simply send simple text from my PC to the Arduino via WiFi and to get back some defined feedback the same way?
How to construct a simple program to manage it?

What other hardware do I need to simply send simple text from my PC to the Arduino via WiFi and to get back some defined feedback the same way?

How would you send data to a wireless printer? You need some application on the PC that knows how to talk to the Arduino, whether it is a client or a server. The WiFi shield is an ethernet shield without an ethernet cable.

That means that the Arduino can be a server, where clients (like browsers) make requests. Or, it can be a client, making requests of servers, like when you use your browser to request that google cough up some information.

A WiFi shield is not a simple radio where you can send or receive text.

Oh! thank you PaulS

Then I have some problem with my application.

I have the Arduino connected to my PC via USB and I can send there trough some commands (numbers or characters) interpreted by the Arduino to control the relays of a power module.
I thought I could do the same wireless!

Is there another possibility?

Is there another possibility?

Lots. Bluetooth. XBees. nRF radios. 433 MHz radios. Each kind of radio has pros and cons, and all have been hashed over more than once.

Thanks a lot, PaulS

I see, I have a lot to learn yet.