Hi Jim,
the easiest way is through the developer board, providing your mDot has the 8 way programming header installed. Not all variants do and I had to install this on those that didnt have it.
There is a much simpler programmer that mDot plugs into and it then plugs into a spare USB port but not sure if these are actually generally available yet.
There is a third method which is more the diy approach as it relies on obtaining another cheap mbed based board and using the st-link programmer from that. and is a method I'm currently looking at for future on board programming of mDot without removing them from the board.
The common thing with the above methods is they all rely on the st-link programmer appearing as a flash drive, the compiled code is then dropped onto the drive and it reflashes the mDot.
Thanks
Andrew