Um, google I2C, SPI? That should get you started with the most common stuff. Once you "graduate" from that, you can start looking at the higher speed stuff, like LVDS.
Re LCD - depends. If it is a standard module, it is likely controlled by one of those Hitachi HD44780 chips (possibly under a blob of goo), those often have a standard pinout too. If not, then it could be a completely custom affair and good luck trying to reverse engineer that. Unless it is a particularly nice display, I wouldn't bother - a new LCD costs a few bucks and you know what you are getting.