Well, the 1602B-TMC-JP is a parallel unit and a serial version is not available.
You have a few options to connect your LCD to a computer, but you will deffinatly need at least some knowledge and skills with basic electronics.
Firstly, you obviously need a Parallel 16x2 White LED Backlit (CFAH1602B-TMC-JP) LCD, which you can order from CrystalFontz -
http://www.crystalfontz.com/cgi-bin/pricing.pl?product=1602b-color
To connect your LCD you have a few options;
1) Firstly, you can purchase a special backpack type device which you connect to the LCD and it makes it serial. It's then just a matter of plugging your LCD straight into the serial port on your computer.
This is probably the better option and will save a lot of time and effort on your part.
You can buy these adaptors from a number of places, the most popular is the "Wirz backpack" -
http://www.wirz.com/products/0128/index.html
This will also mean there are a lot less wires etc. and you can also use software which supports serial LCD's only (ie: LCD Driver 1.0 -
http://lcdriver.pointofnoreturn.org )
CrystalFontz have also put together a guide showing the Wirz backpack method here:
https://forum.crystalfontz.com/showthread.php?threadid=214
2) The other option is to wire it directly to your parallel port.
To do this you need a parallel cable, soldering iron, a fair amount of soldering skill and a lot of paitence and care..
You basically solder one end of the parallel cable directly onto the LCD.. obviously this method is a fair bit more dangerous than the backpack route, and also a lot more time consuming.
If you decide to take this path here is the most commonly used schematic:
Remember that both of these methods require a fair amount of electronics skills and if you are not absolutely confident then you are probably better to go with a natively serial LCD.
Good luck
