if this is the first time ure dealing with electronics and interfacing with parallel/serial ports you shouldnt have started with an lcd imo. lot of new modders do the same mistake by jumping right into the complicated stuff and get overwhelmed in the beginning. i think the tutorial that i gave u explains it very clearly and i know i could do it.
There are some basics you have to know. the lcd needs to be powered and there are pins for its essential setup (main power and ground, backlight, contrast etc..) then you have the data pins that tell the lcd what to display. everything is listed in the specsheet, each pin function and even the characters and commands for programming. i havent done anything like this in life and i cannot tell you anything for certain.
i dont think you can hook it up to the serial port since it has 9 pins and the lcd has 16 plus power, but after all, you only need 8 data pins i believe.