Image “noise” refers to random artifacts found in some images, normally as a result of a high iso (sensor sensitivity) setting. In the image below taken at iso1600, noise is evident as a random pattern of multi coloured blotches.
The good news is that there are ways to minimise noise when setting your exposure. The simplest way is to manually setting the iso to the lowest setting, usually iso 100. The setting used depends on the application as lowering the iso will reduce shutter speed which in turn may lead to blurry images in low light if you are shooting hand held. Read more about camera exposure.
When shooting long exposures in low light, I manually set the iso to 100, use a tripod and remote shutter release or the 2 second timer. The iso setting minimises noise, the last steps ensure the image is sharp. If your camera has a control for noise reduction for long exposures, you might want to experiment and see if this helps. The image below has been taken at iso 100 using the techniques above and no noise reduction has been applied.
When shooting people in low light I set iso to 100 use an external flash with a diffuser and usually apply flash compensation reducing the amount of light applied from the flash (negative compensation) so that the flash is providing a natural fill rather than nuking the subject. This results in a more natural looking image and minimises noise. Check your manual to learn more about flash compensation and experiment. Note that it is likely that there will be light falloff (darkening) in the background when shooting like this in an uncontrolled environment. Setting to iso100 will help minimise noise in these situations.
If there is noise in your image and it is intrusive you can remove it with software however this tends to smooth the image leading to loss of detail. Sharpening slightly can restore some of the detail but its a balancing act between how aggressively you want to remove noise and how much detail you wish to preserve. Applying too much sharpening can also destroy an image leading to other undesirable artifacts. Below the same image showing the effect of noise reduction in Lightroom on the right. There are numerous tools that can do this, its just a question of finding one that works for you, however the best way of dealing with noise is to minimise it in the first place. Using the techniques described above should assist.