LCD controller interface
These custom LCDs have different drivers and communication protocols. You need to find out:


the type of driver chip, 
a datasheet of the driver chip (this can be problematic)
actual LCD arrangement (a driver chip supports multiple arrangements)


Then you can start the show. Usually you need to shift in 24 bits (or 16) on a parallel (or a 8 bit) interface to control each pixel. Note that these bigger LCD screens have no full screen display ram, so you need to refresh the screen pixel by pixel regularly - just like a classic CRT. 

Therefore for these bigger LCDs usual hobbyst grade solutions such as using a microcontroller, or an Arduino will not work. Just count up the number of pixels and do the math - it might need 200k of ram just to store the display memory, not to mention the referesh requirements. 

You need more juice for that. Consider e.g. the old PXA255 which has a built-in display driver via DMA channel to drive these kind of LCDs. You may refer to the datasheet of PXA255 or PXA270 to learn more about this topic.

It can be quite hard, and definitely not the next project after 16x2 standard LCDs :)



However, there is a solution! Because driving those LCDs are so awfully complicated, many companies have developed their own drivers which will off-load all of this mess from you.

Check out 4D systems http://www.4dsystems.com.au/ as they have solutions which reqire only a serial port wire to drive these nice displays.

FTDI also developed their own stuff called EVE, and sell integration-ready LCDs http://www.ftdichip.com/Products/Modules/EVEModules.html and http://www.ftdichip.com/Products/Modules/EVE2Modules.html (This latter looks very similar to the LCD you have found.)

Unless you have a 32bit microcontroller with megabytes of memory and a DMA enabled dedicated display port, this is the only feasible way to go, I am afraid so.