Camera selection can be a tricky business especially if you launch yourself into it without a bit of forethought and at least some basic knowledge of the "in's and out's" of digital cameras. There's dozens of manufacturers, hundreds of different models and a myriad of technical specifications.
At the very least you should have a basic understanding of the jargon used to describe digital cameras, eg
Make and Model
In terms of a particular make and model, my only advice is stick to a leading brand which has some history with digital cameras, examples of such brands are ( in alphabetical order only ) Canon, Nikon, Olympus and Sony.
Note: I've only mentioned these 4 as
examples, there's no implication that other brands are inferior or anything else. Just that these are brand names you will find it impossible to avoid and it's very likely that you would find a camera which is to your liking within the range offered under these brands.
Personal Needs
Even if you don't have a clue about technicalities, at least consider any special requirements you might have beyond ( say ) casual family snap shots, eg. taking photos of sporting events, a camera which will easily fit into your pocket, etc AND how much of your hard earned you are willing to part with.
Do you already own some accessories used with an older camera which are still in good condition, eg. flash gun, batteries, or lenses from an SLR film camera, will these be compatible with your intended purchase ?
SLR or compact
Modern digital cameras are "officially" categorised as compact or SLR
*, according to me "compacts" are split into compact and "pretend SLR", ( the latter look similar to digital SLR's but are generally cheaper and lack some of the features/facilities of SLR's ).
From a non-geek's point of view, within the various categories there's little ( if any ) discernable image quality difference between similarly
R.R.P. priced cameras from any of the top brand names within the ( 3 according to me :-) )
categories. So in the absence of any particular brand loyalty or existing accessories, once you've assessed your particular needs and decided how much you want to spend, it's time to look for the best deal you can get.
*Note: SLR is an acronym for Single Lens Reflex which simply refers to a camera which doesn't have a separate viewfinder lens. When you look into the viewfinder eyepiece you are looking out through the same lens that takes the picture. As many compact digital cameras work this way, they are in a sense SLR's too :-). The term "SLR" is used colloquially nowadays to describe digital cameras which have interchangeable lenses and prices which start where compacts leave off, around AU$700.
Viewfinders
Many modern compact cameras don't have an optical viewfinder/eyepiece just an LCD preview screen which also serves as an information display.
Does this really matter ?, yes it can. The images displayed on small LCD's, ( even the backlit ones ) are at best difficult to see outdoors on a bright sunny day unless you can find a shady spot, ( think about mobile 'phone displays ).
A conventional eyepiece viewfinder has the advantage of providing a highly visible preview in any lighting conditions so keep this in mind if you're going to take a lot of photos outdoors. The advantage of an LCD "viewfinder" screen is that you're not limited to keeping the camera right up to your eye.
Photographic Retailers
Buy your camera
from a specialised photographic retailer face to face, this does not include large retailers who "specialise" in everything from furniture to home theatre systems. That might sound unfair but the fact is that when it comes to the actual purchase, particularly if you're a still a bit "iffy" about the selection you've made the staff at specialised photographic retailers will have in-depth product knowledge, are typically experienced enthusiasts themselves and you'll find their advice
invaluable. Even the asking price is a few dollars higher ( and it'll almost certainly only be a
few ) you'll be doing yourself a favour, trust me on this. Explain why you've selected a particular camera or can't decide between a couple and don't be afraid to ask if there are any "stand-outs" either good or bad,
don't just walk in and ask for their recommendation!
Terminology
There's really no getting away from at least some basic photographic terms and it's worthwhile being familiar a few of them.
Zoom
Expressed as a multiplication factor, eg. 3X, 5X, etc. Zoom refers to how wide ( or narrow ) the lens' viewing angle is, the larger the number, the greater the focal length and hence the narrower the viewing angle, in other words how much "close" there is in close-up :-)

Eg. Here's a picture of a 3X zoom lens. Note the focal length is 6.3 - 18.9mm and 18.9 is 3 times 6.3 !
Focal Length
Also applies to lenses, is expressed in millimetres(mm) and relates to the magnification factor or how close the subject will appear in the photo, eg. 4.7mm, 6.3mm, etc., the larger the number, the closer the subject will appear.
Sounds simple enough doesn't it ... well, there's a bit more to it when it comes to comparing different cameras. If you read the specifications for a digital camera the focal length figures along with those for the actual lens there will usually be a 35mm ( film SLR ) camera equivalent and it's best to use this equivalent figure to properly gauge any comparison.
If you are looking at ( what I call ) compact cameras go for one that has a minimum of 27 - 28 mm equivalent. This gives a good wide angle view for landscapes and with even 3X zoom the ability to take close-up shots of smiling faces.
Megapixels
A pixel is a single
Picture
Element. An "x" is used to indicate a plural and mega is a prefix meaning 1 million. So for example an 8 megapixel ( 8MP or 8MPx ) camera will have an image sensor with 8,000,000 elements, each element making up 1 pixel.
It's an indication of the amount of detail a camera can capture, commonly referred to as resolution, the more megapixels the higher the resolution ( in theory anyway ). Basically the more megapixels the better, but as always there's a bit more to it. If your mainly interested in printing your photos "things" get a little more "interesting" :-)
Staying with the 8MPx example, if you're wanting to print a photo even as large as ( say ) A4 then 8MPx is enough to produce a high quality picture. It follows therefore that anything over this will be more than enough. It is worth noting that (
all else being equal ) the difference in the results achieved by 10MPx and 12MPx cameras is negligible and this should not be used as a make or break criterion.
This is especially true if you're mostly interested in viewing your photos on a monitor ( even a
very big monitor ) or a digital photo frame.
more to come ...
Buzz Words
Digital camera marketing has given rise to a lot of "gee whiz" terms for the various in-built features/functions of modern cameras. I'll do my best to decipher some of these later ....