How to Communicate between arduinos wirelessly?
You can use XBees. They are powerful and do provide wifi connections (the recent versions).

And you rely on well-designed devices which guarantee packet retransmission and they achieve up to 1km in an open field. 

XBee still works with serial communications making them an excellent tool for your embedded project. 

Just plug your Arduinos and write code to send/receive data. This library is a good start point for API mode.

If you don't mind using all the benefits from ZigBee protocol, just use AT mode where all you push in one side is sent to another via serial communication.