This instructable will teach you how to use the normal digital camera you already own to take night photos that are not blurry, and without a tripod. Don't believe me? The photos on this page were shot just last week with my digital camera without a tripod. Read and learn, grasshopper! And press the "+" sign on this instructable so I can get closer to winning that dad-gum laser carver thingee.
(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
By basic settings, I don't mean resolution, zoom lens, or movie mode. The only settings you will need to control are ISO, exposure time (shutter speed), aperture and shooting mode.
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)