When shooting in low light conditions, we generally have to compensate for the lack of light in the scene by bumping up our ISO setting. This is great as it allows us to shoot without using flash, but the problem with using these high ISO's numbers is that it can introduce noise to your images - the stuff that looks like grain or speckles. This puts a lot of people off shooting with high ISO's, but there are a couple of things you can do to minimise the noise and get the best images in low light......
1) Get more Light
The easiest way to not get noise is to keep your ISO setting reasonably low in the first place. To do this, try to physically get more light on your subject - open the blinds, shutters, or move your subject to a location that has a bit more light coming in. Although you could try using a slightly slower shutter speed or a wider aperture, you need to be very careful that by doing so you aren't swapping one problem for another! If your shutter speed is too slow, that can cause motion blur which will result in a "soft" picture. Similarly, too large an aperture might also give you problems, as it can be difficult to get precise focus, and you can end up getting an eyebrow in sharp focus instead of the eye! You can fix noise in processing to a certain degree, but not missed focus and motion blur, so I would rather have a noisy image than a soft one. So, get your subject into the best light you can, set your aperture and your shutter speed as you need for the picture, and once you have done all you can in that regard, use the ISO setting you need to get a correctly exposed picture - even if this means a high ISO.
In the image above - which was taken as a test image - you can see how close I have my subject to the light source, in this case the window. This meant I could use an ISO of 640 even though it was dull and overcast outside, and there was not a lot of light in the room. Had we moved further away from the window, I would have needed a higher ISO.
2) Expose Correctly In Camera (Or Over Expose)
Under-exposing in camera is the biggest reason for having excessive noise in your photos. Many people are scared to use higher ISO's for fear of introducing noise (and I have been guilty of that too) but as noise lurks in the shadows, when you raise the exposure in processing, the noise becomes more visible throughout your image. I always expose to the right (meaning I over-expose a little bit from what my meter is telling me) when shooting in low light conditions so that I keep noise to a minimum. Here is an example of an image taken with the same aperture and shutter speed, but where I've changed the ISO to get different exposures. In the first I've underexposed but brought it up to the correct exposure in processing. The second was exposed correctly in camera and the third was slightly over-exposed. again with exposure corrected in Lightroom. All 3 are cropped so you can see the noise levels easier.
It's really hard to see sized for the web, but hopefully you can make out that the underexposed image has the most amount of noise visible when brought up to the correct exposure in processing, and actually, the slightly over-exposed image has the least amount of grain, even though it is using a far higher ISO. So don't be scared of ramping up the ISO to get the exposure right - it will pay off in the end!
3) Reduce Noise using Reduction Sliders in Lightroom or ACR
These sliders are identical in Lightroom and Adobe Camera RAW (The free photoshop / elements plug in) so the method is the same regardless of which program you use. Below is an example of what can be achieved by using the sliders correctly. The cropped image at the top is after processing using this method, and the one on the bottom is what it looked like if I had just left the sliders at their defaults (always look in the shadowy areas when assessing noise)
Again, it's difficult to see this clearly on the web but hopefully you get the idea. Here is the final image, converted to black and white.
Here is a tutorial by Digital Photography School on how to reduce noise in photos using the noise reduction tools in Lightroom (same steps for ACR)
4) Embrace the Grain!
Some photos can look great with grain - in fact, some photographers add noise for the texture it adds to their photographs! (you can see this post on adding noise for creativity if you are interested in this) Personally, I think this looks best on black and white images, so if I have a noisy image, I tend to convert it. Sometimes when taking the photo, I try to also imagine the scene in black and white, so that I can compose in camera with the final outcome in mind (that's not to say I manage it successfully, but I give it a go!) Moody / dramatic black and whites look great with a bit of noise, as it generally doesn't detract from the image at all.
5) Upgrade to A Full Frame Camera
I've included this last as I suppose it is a bit of a cop out! But the truth is, full frame cameras handle noise much better than crop frame sensors. There is a world of difference between my 5D Mark III and the Rebel that I used to have. That said, I wasn't really aware of all these noise reduction techniques when I was shooting with a Rebel, so I think these would have made a massive difference at the time. It's also worth noting that the MK3 handles noise beautifully but you can still get a noisy image with this camera even at lower ISO numbers if you don't expose correctly, so I always at least try to get this right whilst shooting. So, upgrading your camera is a option to help you handle noise, but I would try these techniques first if you are using a crop frame, and you should see a difference in your images.
I hope you found these tips on how to reduce noise in photos helpful!