3) Experiment with switching away from the auto-everything modes
Once you understand the basics of shutter speed, aperture and ISO, you’re free to swim in the deep end of your camera’s capabilities – the creative modes. Leaving the camera in auto-everything (often shown with a green box on the mode selector) will give you passable to good shots, but you’ll never really know in advance what you’ll get because the camera decides on depth of field and shutter speed issues (and ISO on some cameras).
I’d recommend getting comfortable with Aperture Priority mode first. In this mode you control the aperture and the camera will choose a shutter speed to give a properly exposed shot. Choose an appropriate ISO for your lighting conditions (higher for darker), and see what you come up with at different apertures – keeping an eye on the shutter speed to guard against blurring (unless that’s what you’re after).
4) Switch off the on-camera flash
On-camera flash tends to be very unflattering, creating a harsh flat light on faces, and ruining the atmospherics of a scene. Cameras these days are getting astonishingly good at shooting in low-light situations, and you’ll get much more satisfying results if you increase the ISO and shoot without the flash.
I’d take a little bit of noise on a warm and inviting shot taken without a flash over a crisp but cold shot taken with one.
5) Try an inexpensive prime lens
If your camera came with a kit lens (one bundled with the camera body), it’s likely a medium zoom lens, that covers a pretty useful range. It’s capable in most situations (especially outdoors), but likely isn’t as good in lower light conditions (because its lowest aperture might be f/4 or above), and the image quality might not be stellar.
Canon, Nikon and Sony each make 50mm prime lenses that are pretty affordable (‘prime’ simply means a lens that shoots at a fixed focal length, rather than a zoom that shoots at a range of lengths, such as 24-70mm). Experimenting with one of these will let you work with a much narrower depth of field, use a faster shutter speed in lower light and might give you better overall image quality than a regular zoom. I was amazed at the images my old Canon Rebel XT could produce with the plastic Canon EF 50mm f/1.8 lens.
However, be warned: these prime lenses have acted as gateway drugs for many people (myself included) – leading them down the path towards much more expensive and esoteric lenses.