Flashing Smoothie to your board depends on your board type :

mBed

Simply copy the main.bin file to your the USB Mass Storage disk the mBed shows up as.
It must be the only .bin file there.

LPCXpresso

Connect to the LPCXpresso using a serial cable. TODO:Instructions
Do "make flash" in the Smoothie folder.
Then put the LPCXpresso into bootloader mode. TODO:Instructions