It's taken a while for digital cameras to 'arrive'. Over the past few years we've had little more than excuses for cameras, devices that might have been praiseworthy if only they'd had higher resolution or if only they could shake off the strange green/blue hue pictures have when taken outside.
Nowadays the very best digital cameras have over three million pixels which they use to capture an image. They can handle colour balance well and, in some cases, better than standard 35mm print film.
But first let's examine the basics. A digital camera is essentially little more than a standard camera without the film. Instead, a small optical microchip (a CCD, or charge-coupled device, array) is placed behind the lens and this is used to capture the image. The standard shutter and aperture arrangement of an ordinary camera is still in place, although the microchip has slightly different image capturing characteristics compared to standard film. Not that you'll notice, because digital cameras operate identically to standard 35mm cameras - you simply 'point and click', although digital cameras can tend to be poorer in low light conditions such as dimly lit rooms.
When the button is pressed, the image is recorded by the microchip and passed immediately to the special 'flash' memory, which stores the data even when the camera has no power (such as when the batteries run out or are removed).
Digital cameras have a viewfinder like a normal camera and also usually have a small LCD screen, a little like modern video cameras (which in fact stole the idea from digital cameras). This provides a 'through the lens' preview of what's about to be photographed and can also be used to control the functions of the camera, such as fine tuning exposure, via a menu system.

However, most importantly, digital cameras look like traditional cameras (well, most do) and they act like digital cameras. You look through the viewfinder, tell the subject to say cheese and press the button. No fuss and no bother.
As mentioned above, a digital camera is measured primarily by its resolution - or detail - which at time of writing tops three 'megapixels' (i.e. million pixels) on the latest cameras. This will record eyelash-level detail in the average picture, which is all most of us need. However, soon the standard could be four megapixels or five, six, or seven - technology is marching at a fair old pace, largely because digital cameras are more popular than ever.
Buying a digital camera requires patience. There are many things to consider. Ideally you'll want to examine a picture actually taken by the camera to see how well it handles colour and how sharp the picture is - use photo editing software and a magnify tool to zoom into close detail. Is the picture sharp all over?
You also need to consider how much memory the camera has. For example, a 3 megapixel camera with 16MB of memory will only store around 6 images at top resolution. This will double with a 32MB camera, while 64MB will allow 24 top quality pictures - still not a huge amount but as good as you're going to get because the memory used in cameras is pricey. Also consider how the memory can be expanded - how costly are add-on memory cards (usually CompactFlash)?
Consider the size and quality of the LCD screen but also consider battery life at the same time. The LCD screens on the back of most cameras sap batteries, meaning that you literally get around half an hour's use before the whole thing packs up. Therefore a rechargeable battery is a must - make sure the recharge time is reasonable (in the order of a couple of hours rather than a couple of days). Battery life can be vastly increased if you solely use the viewfinder and avoid the LCD screen, by the way.

How does the camera connect to your PC? A USB connection will transfer the picture data faster than a serial or parallel port can. What about the free software? Do you get a good image editing package thrown in so you can tweak the pictures afterwards and remove the red-eye/crow's feet from faces?
After these considerations, more traditional camera buying concerns come-in. Does the camera have a decent optical zoom? Can it zoom beyond the traditional limits of 35-70mm (at 35mm equivalent)? 'Digital zoom' is an interesting idea, by the way - it zooms into the picture to allow more detail but reduces the resolution - but it's rarely useful. Does the camera have a 'macro' mode so it can zoom into objects at close range?
Can you both automatically and manually control exposure? Are you able to take 'burst' mode shots (i.e. a couple of shots per second, useful to capture the action on fast moving sports?).
Finally, consider the price of digital cameras. They're expensive. They always have been expensive and, unless the price of memory falls (which has been much rumoured but hasn't yet occurred), they'll continue to be expensive. You generally get what you pay for, however, and a good digital camera will be worth the expense.
Now read our Digital Camera and Camcorder reviews