What is the best way to douse a charcoal grill?

Add some coals over the hot ones and/or reduce airflow some other way (many grills have slits or vents to control airflow, play with those, close them partially).

Both should reduce heat output (adding coals of course will mean the grill will burn for longer and will eventually heat up again).

I'd not throw water or other liquids on it. Only makes a mess :)

South American style toss salt over the coals. Works well, looks sassy, but makes a big salty mess

More practically just use fully combusted cold ashes from previous fires. Gently scatter them over hot coals to reduce airflow and lower temperature for a while. Use a large tin with big holes punched in the lid to makes handling and shaking easy, or just get messy and scatter by hand

Hardwood ashes that have been quickly sifted should not be too dusty so as to make a mess with the food

Instead of dousing the coals, in a primitive setup, you would be better served to manipulate distance from heat source as your form of temperature control. It can be as simple as adding or removing bricks to space your grill from your flame, or as complicated as a pulley-based system to raise or lower your grate.

Using water will cause your coals to smolder, which can give off creosote (less likely with charcoal than wood, but still a possibility). This can impart a rather nasty flavor into your food.

If you are unable to or uncomfortable with changing your grate distance, then salt or some other dry smothering agent would be viable.

Heaping some pre-soaked (apple, etc) wood atop the embers cools coals and creates steam and smoke. For more info, read up on smoking food in a barbeque.