Both the 3pi and that module run at 5V, so there should be no problem with voltage levels. Your RX/TX connections are backwards - RX on the module should connect to TX (PD1) on the 3pi, and TX on the module should connect to RX (PD0) on the 3pi. You will definitely need to connect GND to GND. PD1 is shared with the red LED, so it will be mostly lit when you have enabled the serial port on the 3pi.
Beyond that, I would have to see a datasheet or User's Guide for the module to give you advice. Do you have a link to one? For example, the CC2500 module might have a built-in regulator, which would mean that you could power it from the 9.25 output on the 3pi. There might also be pins, like a reset line, that need to be connected.
By the way, I recommend taking a look at the serial slave program for the 3pi to get ideas about programming your communication protocol.