Taking a photo is easy—you just push the button. Taking a good photo involves understanding a little about how cameras work and what their limitations and capabilities are. Every camera is essentially composed of the same three elements: a sensor which turns light into a recorded image, a lens which gathers and focuses light on the sensor, and a shutter which can open briefly to expose the sensor to light. These three elements each have characteristics that impact the quality of your photos.
Sensor
Sensors in digital cameras vary from about 24mm wide in professional “SLR” styles to roughly 5mm wide in camera phones. Since sensitivity is proportional to the area of the sensor, that means camera phone sensors are typically only 5% as sensitive to light as their larger cousins. The good news is that silicon sensors have advanced to the point where that 5% still can be very effective. In fact, Fujifilm has announced a compact digital camera with very high sensitivity (ISO 3200) at 6 megapixel using a sensor only 7.6mm wide. Still, it's reasonable to expect to need more light for small cameras, and most camera phones require relatively good light conditions to produce a sharp and low-noise image.
Trend to watch: higher sensitivity with low noise. All the sensor manufacturs are pushing to produce cleaner images with less light. Look for these 'high ISO' capable sensors to grow in popularity as consumers see beyond the 'megapixel count'.
Lens
Lenses are the heart of a camera. No camera can be better than its ability to focus light on the sensor. Several of the early camera phones advertising 1.3 megapixel resolution were actually worse than their 0.3 megapixel VGA predecessors for lack of a quality lens. In fact, lenses can be quite complex and the design and manufacture of lenses represents its own art. A modern wide-range SLR zoom lens such as Canon's 24-105mm has 18 elements (carefully formed pieces of glass) arranged in multiple groups to provide both a broad focus and zoom range with consistent light-gathering ability. Compact digital cameras have scaled down and simpler lens packages - the Fujifilm F30 mentioned above has a 6-element lens offering a range of 3x zoom with a considerably smaller width (or aperture). This still enables resolving a autofocus range of roughly 2" to infinity. Camera phone lenses are even more space constrained and typically have only two to four elements. Most 2 megapixel camera phones have four elements cameras although some are fixed-focus with one or two elements. Without autofocus, getting a sharp image requires positioning the camera within the fixed focus range of the camera, which is typically between eighteen inches and ten feet of the subject. You can test various distances using a test image at http://www.checkmycameraphone.com/
Trend to watch: folded optics. Some camera makers - Sony and Panasonic for example - are producing zoom lenses which don't extend beyond the camera body. These 'folded optics' lenses enable thin and compact packaging with a zoom lens.
Shutter
The shutter mechanism isn't as critical as the time the shutter is open. A shorter exposure time allows for less light capture but offers less chance of motion to cause blur. A longer exposure time results in a brighter image but potentially motion blur. A rule of thumb is that a hand-held camera exposure should be no longer than roughly the inverse of the 'focal length' of the lens - a measure of its light-gathering cone. For an SLR with a typical 50mm lens, a time of 1/100 of second is pretty safe. For the much smaller camera phone lens, the '35mm equivalent' focal length is often less, and an exposure time of 1/60th of a second would work well - if there is enough light to capture the image in that time. On digital cameras you can often see the exposure time the camera has selected in the display. On camera phones it's often not apparent how long the shutter was open, nor can the time be selected.
Trend to watch: image stabilization. By moving a lens element or the sensor to compensate for camera motion, the shutter speed can be significantly longer (over 1/10 of a second in some cases) and a sharp image can still be captured. This technology is quickly spreading and can have huge impact on shooting in low light.
How to take a good photo
1. Get enough light onto the sensor. Especially with a camera-phone, try and work in a place with abundant light or use the flash if necessary.
2. Know your lens. If using a fixed-focus camera, make sure the entire region you are interested in capturing is within the 'sweet spot' of the lens focus. If you are two close or too far, you will lose detail.
3. Hold the camera steady while you capture the image. Even if you can't set the exposure time, you can maximize the sharpness of the image by keeping the camera still during capture.