Lower ISO settings give you less grain
If you’re pictures are noisy, use a lower ISO setting. Modern digital cameras are getting better every year at lower grain at high ISO settings but it is still present – particularly with point and shoot cameras.
Setting your ISO to 100 for example gets clean shots with very low noise. It’s also less light sensitive so you’ll need a tripod if you’re shooting at night.
With film often times the grain look is desired. Unlike digital noise, film grain has a nostalgic and sometimes beautiful look to it. In this case, use a higher ISO to achieve the effect. Pushing your film speed 1 or 2 stops will also increase grain and it will increase contrast as well. For example get some tri-x and shoot it at 1600.