Hi nagarajatmsrit,
Usually SoftSerial is used on the Arduino, so that you can use the native UART for debug and control signals to the computer. On the Galileo, you don't have that problem, as the connection to the computer has it's own virtual serial port over USB.
In most cases (I don't know your use case exactly so I can't say for sure) you can just use the hardware serial connection on Arduino pin 0 and pin 1.
You just have to do a few minor changes to the code, if you have some example code, you can paste it here and I'll show you what to change, if the above isn't enough to get you started.
Hope it helps!
/Thomas