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I am working on a project that uses an Ardunio, a uLCD-70DT touch screen by 4D Systems, and a Sparkfun Bluetooth Mate Silver. From what I understand communication from the touchscreen can either be through the I/O pins on the back of the board (1 I/O pin could correspond to one button on the touchscreen) or through the TX and RX pins to the Arduino. The touchscreen interface will be quite complex so I don't believe using the I/O pins alone will work so it will need to communicate the information about what buttons are pressed and such over serial communication. As far as I know, the Bluetooth module also needs to run over the same TX and RX pins on the Arduino. How would it work using two devices that need to use these serial pins?

Use one on hardware serial and the other on software serial. Or you could find an Arduino board that has more than one hardware serial port, i.e., the Mega.