This is my mantra of night driving during a downpour.
Switch on your wipers. I've seen SO many people who simply don't think about using them. You manhood won't be affected by regular use of the wipers. Also keep the wiper washer bottle topped up regularly.
Switch on your lights, including your fogs, if independently operated switch on the rear ones at least. This is more for the benefit of making yourself visible to traffic rather than improving your own visibility of the road. Your mirrors will mostly be useless and there won't be any point in rolling down the window and cleaning the right hand mirror.
Avoid overtaking, but if you do have to, maybe to overtake a stopped vehicle, don't make any sudden maneuvers; assume that all other vehicles around you can't see even half as much as you, so give them plenty of room.
Be especially careful at junctions with no street lights when making turns, since windows and mirrors will be useless. Push bikes and pedestrians will be all but invisible, although they assume we being in a car have telescopic night vision. And there will always be the odd motorbike with no lights (and usually no brakes) as well.
If it's really heavy rain, to the point you cant make out the difference between the road and the gutter, I usually follow the vehicle in front of me allowing for a generous gap between us.