(sample photo shot at ISO 400, 6/10 of a second, no tripod, of the downtown Omaha skyline)
Step 1: Get a digital camera that lets you control it's basic settings
Relax, you don't have to run out and buy a new fancy-shmancy digital camera to do this. Most digital cameras that aren't the bottom-of-the-barrel or older than 3 years old will let you do this. Usually you just have to set the camera into "custom" or "manual" mode to accomplish this.
If you want to know how to set up these features on your digital camera, consult your owner's manual just like I had to do.
Also, while IS or VR (image stabilization or vibration reduction) can help, they are not necessary. All of the sample shots on this instructable were shot on a several-year old Canon A620 that lacks IS, and only goes up to ISO 400.
If you need to update your camera, and got some dough, I would recommend buying the Canon SD800 IS. If you don't got $300, but have $200, then I would get what I got, the Canon A620. If you only have $100, go on eBay and buy a used Canon A530. All 3 will enable you to do this instructable.
Here are a few guideline definitions that you can skip, but I am including them just so all the photographic "measurebators" don't have a hissy fit:
ISO = how sensitive your camera is to light. ISO 200 is twice as sensitive as ISO 100. ISO 400 is twice as sensitive to ISO 200. The more sensitive (higher ISO) the shorter the exposure needs to be for a similar image. So why not jump to ISO 1600? Because in digital cameras, that will make for a very grainy photo unless you got an electronically cooled CCD like they use for photographing astronomy. Most "normal" digital cameras only go up to ISO 400, anyways. And yes, there is a bit of noise in these photos, but the end results are more than passable when printed on a high-quality printer.
Exposure (shutter speed) = how long your shutter will stay open, allowing light to collect on the image sensor. 1:15 is 1/15 of a second. 1:4 is 1/4 of a second. Remember, in shutter speeds less than a second, the LARGER the bottom number, the SHORTER the exposure (provided that a 1 is the numerator) 6/10 is more than twice as long as 1/4. Also, camera shake can cause blurry photos at settings longer than 1/15.
Aperture: F-stops are different settings allowing different amounts of light to enter your camera. This is different from exposure, in that the aperture is that funky iris/anus looking thing that is a series of connected sheets that either open or contract to make a hole get bigger or smaller. Think of the opening to the old James Bond movies where that aperture starts as a small dot and opens up to get bigger. If you watch the LCD on your camera and adjust the aperture, you will see which setting opens up the iris to allow more light in by watching your LCD become brighter or dimmer.
(UPDATE: No, these definitions aren't taken from Standard Photographic Definitions 9th Edition or New England Journal of Expert Photographic Advice and Medicine. These are thumbnail definitions, and I am not an expert. I am just trying to explain what I think is correct to people that don't know any better. If you know something I don't know, I'm not surprised. Post it in a comment below and show the world how wrong I am.)
(sample photo shot at ISO 200, exposure 1/5 of a second)
Step 2: Experiment with these settings, and conduct principal photography
It is true, that with exposures slower than 1/15 of a second, you will get more blurry photos. But, it is also true, that with exposures as slow as 6/10 of a second NOT ALL of your photos will be blurry.
(UPDATE: and by blurry I am referring to "naked-eye" blurriness when viewing it after it has been printed and from a reasonable viewing distance. If you look at the image pixel by pixel on your computer screen it will probably look blurry.)
So the philosophy I am preaching is this: take lots of photos at a few different settings, and you are DESTINED to have a few winners. Actually, many more winners than you think. And you won't have to take hundreds of photos every time you want to take a nice night picture. The following instructions are only to be used the first time you take night photos, in order to determine which setting for your camera gives you the best results. Then in the future all you have to do is set your camera to your preferred settings, and take 5-15 frames so you can be sure to have one that isn't blurry. It's a small price to pay to finally get to bury that g-d tripod and actually get to capture the cool night shots when you see them.
The first thing you have to do is make sure you have a large-capacity memory card for this. With my A620's 7 megapixel full-resolution size, I like to load a 1GB card. This will be fine.
Second, set your shooting mode to "continuous," meaning that as long as you are holding down the shutter button, your camera is taking pictures.
Next, experiment with these settings: ISO at 200 and 400, shutter speed from 1/15 of a second to 6/10 of a second (or whatever looks good on the LCD as you adjust settings), and aperture set to whichever setting allows the LCD to appear as bright as you want the photos to be. In otherwords, set ISO first, shutter speed second, and aperture to the brightest setting. Now, start taking pictures.
Hold down the shutter so you get 5-15 shots at each setting, experimenting with the variables. Take lots of pictures. Try to hold the camera as still as possible while doing this. Cheat if you have to. Lean against a parking meter, bus stop sign, railing, tree or wall. Sit on the bumper of your car or indian style on the curb. Get as still as you can, but whatever you do, don't lug a tripod with you when you take these shots.
Your first night photography session after reading this instructable should easily net you 200-300 pictures. If you don't have a large enough memory card, then lower your image resolution to the smallest setting just so you can take a shitload of pics. At this point, like the old lie goes, "size doesn't matter." This is an experiment just to see which settings your particular camera loves most for hand-held night photography.
Now, after taking a few hundred shots of your city's skyline at about 10pm, using continuous shutter mode at a variety of settings, go home and prepare to be amazed.
(UPDATE: Upon further reflection, I have reconsidered and logic tells me it actually might work better if you set your aperture (F-stop) to the widest setting first so that the most amount of light is entering to begin with. "So is that the large F-stop number or the small F-stop number?" I have no idea. It is whichever setting makes the LCD the brightest as you adjust it. After you got the F-stop opened up, then set the ISO, then the shutter speed or exposure or whatever it is called on your digital camera.)
(sample photo shot at ISO 200, at 1/4 of a second)
Step 3: Pick your ponies, and brag to the local photo developer
This alone should pare your 300 photos down to about 50-100 photos.
Next, go through the photos zoomed in a little (NOT zoomed in at pixel level though) and look for only "The Best" ones. In other words, if you don't say "wow!" when you look at the photo because it is still a tiny bit blurry, or it is too dark or something, then get rid of it.
This second culling by saving only the best photos will further reduce your pool to probably 20-50 photos.
Now, look at these remaining pictures one at a time, and pick your top few pics, throwing the others out.
After you do this, then look at the "info" part on each photo and rename the pictures to the settings for ISO and shutter speed, just like I have done with all the photos for this instructable.
Now, all that is left to do, is burn these pics to a disc and run around your neigborhood getting reprints made at any local photo counters and compare the results. I took my pics to a high-end camera store in my city that prints photos called Rockbrook Photo, Wal-Mart, Target and Walgreens and made 8x10s of all 4 of my favorite photos. The prices ranged from $5.99 at the fancy camera shop to $2.50 at Walgreens. Results: #1 is Walgreens, a close #2 is Wal-Mart, and nobody believed me when I told them I shot the night pictures on a digital camera without a tripod.
Now because of this experiment I now know exactly what settings to use on my camera next time I see a great night shot. But REMEMBER: with these settings you still have to use continuous shutter mode and be sure to take a good 5-15 shots at this setting because most of them will be blurry, but not all of them.
Now go forth tonight, take pictures of your boring-old skyline, and then make the counter people drool at your local photomats when you tell them you shot those beautiful night shots with your normal digital camera without a tripod. AND, vote for this instructable so I can win the laser-carver thingee! AND AND, post your cool night-pics as a comment to this instructable so I can justify to my family that the time I am spending making instructables is making a difference in people's lives, albeit, unknown stranger-people that are also shunning their family.
(sample photo set at 400 ISO and 1/10 of a second, no tripod)