More noise appears at higher ISO levels.
So keeping ISO low is important in a general sense. However note that noise visible on a screen when you view the image in great detail won't normally be visible in prints or even o screen at normal viewing sizes - i.e. viewing the image as a whole.
So maybe you're looking at the images too closely.
Now you may also be seeing motion blur, which is when the subject moves during the exposure. That's dealt with by raising shutter speed.
Here's the catch :
You can trade between aperture ( f-number ), ISO and shutter speed. However, if the light level is too low ( by the camera's standards ) you could end up trading e.g. a slow shutter speed for a low ISO level. That might introduce motion blur instead of high ISO noise.
When the situation gets like that there are two solutions :
- Flash. Moving subjects ( or humans "standing still" ) close by.
- A tripod, longer exposure and low ISO. This is for e,g, landscapes in low light.
But you can't always have what you want.
A slow shutter speed can also introduce shake blur.
A wide aperture ( low f-number ) will result in a reduced depth of field, which means less depth into the image will be in focus. This is less of an issue with compacts.
Compacts have small sensors and noise becomes apparent very quickly, a little more so on a relatively old one.
You need to learn about exposure and depth of field and flash to balance these options.