There are two major parts to working in low light, and a few supplementary tricks. The major parts are keeping the camera still, and adjusting settings to be as generous with light as possible. You're always working with trade-offs, and which part you emphasize most will depend on the situation you're in.
The most effective way of keeping the camera still is to put it
on a tripod. Your first and foremost goal in getting a tripod is to have
it when you need it; a cheap tripod is a lot better than no tripod at all.
One of these shots of neon on the building I live in was taken with a cheap
tripod; the other was taken with a mid-range tripod, a Uniloc. I own the
more expensive tripod partly because the cheap one broke, and partly
because
the Uniloc offers the ability to do low positioning for macro photography.
More expensive tripods are more stable, but frankly, for night shots on
a lightweight digital camera, the cheap one would have been just fine for
somebody who could avoid banging it into things.
Most of the time, I don't have the tripod with me, which means I have to use something else to keep the camera still. A monopod is more portable than a tripod, and easier to readjust; I have one that I sometimes use, and I'm utterly tempted by getting a really spiffy portable one. Most of the time, however, I have no official camera support with me, and I need to use what's available. The first choice is to actually rest the camera on a flat surface, whether that's a table or a windowsill. Next, I'll try resting the camera on a wobbly surface, like the rounded top of a car or a parking meter, or the arm of a couch. Quite frequently, I'll sit down and rest the camera on my leg. If I'm photographing through the window, I'll press the camera to the window, which both stabilizes the camera and gets rid of reflections. You may be limited in stabilization positions if you have a camera with no LCD or with an LCD display that isn't moveable; I photograph with a Nikon 995 with a swivel lens, making it easy to to put the camera in my lap and turn the LCD to face me. If the camera is self-supporting on a tripod or a flat surface, it helps to use a remote control, so that you don't shake the camera when you press the shutter button.
These three photographs are Melbourne's chinatown arch, 1/2 second exposure at 400 ISO taken with a monopod; a building at the Royal Melbourne Institute of Technology, 1/2 second exposure at 400 ISO taken with the camera balanced on a parking meter; and a fountain in the Melbourne casino, 1 second exposure at 400 ISO taken leaning against a pillar.
If I can't rest the camera on something, my next choice is to hold the camera as stably as possible, pulling my elbows in to my sides, and then rest myself against something. Sitting down and putting my elbows on chair arms is good; so is leaning against a lamp-post or a wall or anything at all. Lying on the ground works, too, and has the dual benefits of putting you at eye-level with small animals and making you less threatening to them.
You can keep a camera still, but you can't necessarily keep the
rest of the world still, so even if you have a tripod available, you may
still need to get the camera to use faster shutter speeds. This means
making
the most out of the adjustability your camera offers, and may involve
extensive
research into the manual, and a good bit of practice. I had no problem
learning how to set all the things I need, and I can do it with some
reasonable
speed after lots of practice. It is not at all clear that I will ever learn
to undo odd settings when I move back into situations that would call for
something more normal...
The easiest and least risky general adjustment, when it's available, is to adjust the ISO setting on your camera. Most cameras that can adjust the ISO setting have an "Auto" setting, but the camera may well feel that 1 second exposures are much more fun than moving to the next higher ISO. Higher ISO ratings mean more noise in the photos, so you don't want to go any higher than you have to. On the other hand, people tend to find noise much more acceptable than blur; you want to go up high enough to get exposures no longer than 1/8 if you're hand-holding the camera (you will need less than that to get blur-free pictures of people who're moving at all).
You may also want to adjust the camera to under-expose. If you are
taking
genuine night pictures, you definitely want to set the camera to
under-expose,
because its default will be to try to make things average out at mid-grey,
and the result won't be dark enough to look like
a night picture. In fact, if your camera doesn't allow you to control
exposure, but does offer some sort of scene modes, something called "night
scene" or similar is likely to mostly set the camera to underexpose, and
you may want to use it for low-light pictures even when they're not at
night. If you're not taking night scenes, underexposing your photos is
going to mean that you need to fix them up later, and you're going to want
to save them with a minimum of compression to allow for later modification.
An underexposed picture will never look as good as a perfectly exposed
picture, even with later touch-ups, but it will in general look
considerably
better than a blurred one.
Your other choice is to trade-off between aperture and exposure time. In general, a camera that's in program mode will prefer relatively small apertures (which need more light), because small apertures mean that you have greater depth of field (more things are in focus). This makes the camera more forgiving about where you focus. Depth of field doesn't mean a thing if you have a 1 second exposure and camera shake is making everything blurry, regardless of where you've focused, so you might as well try trading it in for a shorter exposure. You may be able to adjust it in what's otherwise your standard program mode, or you may need to go into exposure-priority mode. In the latter case, note that you can easily force the camera to underexpose critically, although most cameras will warn you. Some cameras just won't let you fiddle with this at all.
If you can get a photo that's well-composed, reasonably lit, and only slightly blurry, you can always just display it at a smaller size, where the blur will be hard to see. The Melbourne photos above are by no means pin sharp, but they're as good as you could possibly expect for something hand-held for an entire second, and they look fine as long as they're not too big.
It's often hard to focus in low-light situations, and it's worst if what you want to focus on is back-lit. Some cameras have auto-focus assist lights, which can help a great deal. Otherwise, if you have a mode available where you explicitly set the focus point, using it will help, but manual focus may be your best bet. In practice, I tend to use autofocus in the mode where I can choose the autofocus point. If there's more than one place to put it, I pick the one that's farthest from the background lighting.
If you can't get people to hold still, you can sometimes use the motion
blur; the first of these I intentionally used the blur, in the second one
I got lucky. Note that the ghost effect is on a mere 1/4 second exposure
(at 800 ISO).
