Assuming you are using a particles material:
if you go down into the colour settings, you should enable colour ramp. I haven't used unity's system, but I assume this acts similar. Then create a new gradient.
This gradient is followed over time, so if you want a fade over time effect, you should set white (255, 255, 255, 255) at the start, then at the end do transparent and white (255, 255, 255, 0)
Then over a particle's lifetime, it will follow the colour of the ramp and become more transparent.
hope this helps!