How to put on night mode on a Nikon N75?

Will my picture come out clear? Will the flash go off?

Night mode?

Your N75 is a fully adjustable camera and it is up to your to use the cameras light meter to determine the correct exposures at night.

To produce "clear" photos, you will either need to use shutter speeds of 1/500th second or longer if hand held or use a tripod and remote shutter release

This will depend on what you're shooting at night.

Lot's of movement means you need lots of light. If you're doing time exposure then existing light will work but only if you use a tripod and know how to properly operate the camera for time exposure.
The camera can't move at all… Like this.

Your Nikon N75 35mm film SLR doesn't have "night mode". That's a gimmick found on digital cameras.

Here is a review of your camera: http://www.bythom.com/n75.htm

I use and recommend this site for low-light exposures:

http://www.calculator.org/...osure.aspx

For these I chose the Scene 'Distant view of city skyline or floodlit buildings' and ISO 200:

100mm lens @ f11, exposure for 30 seconds.

200mm lens @ f11, exposure for 30 seconds.

Needless to say, my camera was in Manual mode and mounted on my tripod.

Your camera does not have a night mode. You can adjust exposure to whatever you are taking though. If you're taking people, set shutter speed to 1/60s, aperture to f/8, and use a flash. If you're making star trails, set to shutter speed to B (for Bulb), mount the camera on a tripod, set to f/5.6 then leave it on for about 30 minutes.

Night Mode? That sounds like a digital camera term.
RTFM!