You have to do this in small (???) steps.
Start out with an Arduino driving an LCD such as shown in the tutorial at http://arduino.cc/en/Tutorial/LiquidCrystal
Modify this setup so that you can display messages sent from your computer using Serial.read().
Get another Arduino, wire the two serial ports together so that messages generated by this second Arduino are displayed on the LCD driven by the first Arduino.
Replace the wire link between the two Arduinos with the (expensive) RF link that you have referenced.