As light levels decrease exposure becomes more critical because of the way digital imaging works.
Under exposure makes image noise more visible.
Increasing exposure post process also makes image noise more visible.
So 'fixing' exposure post process often seems to add more image noise.
To evaluate an exposure we use a Histogram of the photo. DSLR cameras can display a JPEG Basic thumbnail histogram on the camera's rear LCD.
As mentioned you'll likely need to add light to the scene you are wanting to photograph.
Lens aperture, along with shutter speed and ISO, will affect exposure but has no direct effect on image noise.
What do you mean by a 'low' aperture.
A wide (fast) aperture is denoted by a number like f/2, f/2.8. f/3.5.
A small (slow) aperture is denoted by a number like f/11, f/16.
The numbers above are fractions, so f/2 (1/2) is a much bigger number than f/16 (1/16) is.
There is a digital photo exposure concept known as Expose-To-The-Right or ETTR.
Optimizing Exposure
ETTR
Digital Exposure Techniques
http://www.adobe.com/digitalimag/pdfs/linear_gamma.pdf