I recently started trying to get Xbee to work with Galileo. For a while I was thrown off since Serial1 is mapped to Arduino D0 and D1 (not Serial). By connecting Xbee Serial out Tx (pin 2 on Series 1) to Galileo digital pin 0 and Xbee Serial input Rx (pin 3 on Series 1) to Galileo Digital pin 1. I used the Xbee Arduino library in API mode and it works.
LarsR suggestion above is a good way to test without Xbee to make sure you are communicating with the serial port you think you are. That is similar to how i realized I was using the wrong pins when trying to use Serial and Serial1
