I want to create some sphere with rgb lights that can be controlled remotely.
Something like this http://www.blendid.nl/index.php?id=19
I don't know where to start. Could someone guide me what I need to make wireless control like in project above.
Those Wixels look like a very cool concept; the concern I have is cost and size. You would need a wireless module, arduino, and LED driver for each one. What's your budget like?
As low as possible with good quality
Infrared is dirt Cheep. Line of sight though.
I would guess that you won't get much change out of $70 per pixel for this.
Build a standalone arduino (like my Mini-uino), run at 8 MHz, 434 MHz Rf receiver, 2 li-ion batteries in a AA battery holder.
Overall size driven by the batteries.
Wireless transmitter for control using the same parts.
I was wander if it's possible to use Xbee w/o arduino on receiver side. They say 8 digital IO pins, probably it could run as a bridge RF->LED.
Overall size driven by the batteries.
Overall number of pixels driven by depth of pocket 
I'd go with @Crossroads suggestion. 433Mhz RF links are cheap and make a good starting point, but I think you may run into issues using more than two of them at a time though. You can pick up a 2.4Ghz Nordic nRF24L01 which would be fine with multiple units. They are under £5 on ebay at the moment!
Tiny24 might be a way to go with those RF modules ... Use the SPI for the RF modules and pins for RGB LED(s) ... resistors, button batteries, might be able to get it done within $10-$12 ...
Thats potentially two, for the price of one XBee! Some sort of solar charging ability would be neat.