How does water leave a submarine?

Water is used for a variety of purposes on a submarine, the most common being for depth control (Main and Trim ballast). Main Ballast Tank water is expelled by pressurizing the tanks with either hi-pressure air (emergency blow) or low pressure air from a device known as a Low Pressure Blower. Hi-pressure air is dumped into the tanks during critical casualties when the boat needs to get to the surface quickly; the Blower is used when the boat is at Periscope Depth and can take its time to force the water out. The boat needs to be at PD to use the blower - it has to be able to bring in outside air through the snorkel mast.

Trim ballast is brought in and expelled using mechanical pumps. Like all boats, there is more than one pump in case one fails.

For unwanted water (flooding, bilge water, etc.) another pump is used to pump the water overboard.

Sanitary water - waste water from showers, heads, galley, etc., is forced overboard using hi-pressure air. It's also one of the reasons I don't eat fish.