Using a FTDI to USB adapter with a raspberry pi and a roomba
According to the webpage you referenced, the Roomba has a 5v interface. The cable you linked to is a 3.3v cable. They claim that it will work fine, and it appears to 5v tolerant to receive, but there's no guarantee that the Roomba will accept the 3.3v logic signals as valid. It depends on what transistor technology is used by the Roomba input and I'd give it 50/50 chance it would work with that cable (there's also the chance that it's on the edge and it works one day but not the next.)

However, you don't need to take the chance. This cable is a proper 5v FTDI and would cleanly interface between the Pi and the Roomba:
https://www.sparkfun.com/products/9718

Just connect the Tx from the Roomba to the Rx of the Pi and vice-versa for the other Tx/Rx pair. Then make sure they share a ground through the pin as well. The remainder of the article describes how the author hijacked the 18 volt Roomba power supply to regulate it to a 5 volt for use by the Raspberry Pi.

Once you get it connected, start to read this manual:
http://www.irobot.com/images/consumer/hacker/Roomba_SCI_Spec_Manual.pdf

How you interface depends on what programming language you want to use. I recommend Python, and if so, install Pyserial (http://pyserial.sourceforge.net/) on the Rasp Pi. Then you can use import serial and ser = serial.Serial('/dev/ttyUSB1') to open a connection to the robot. (You might need something other than /dev/ttyUSB1) Then you can send individual bytes to the robot using ser.write(chr(numeric_byte_to_send)) where you replace numeric_byte_to_send with whatever integer you want.