Understanding digital cameras, how do they work?

Well first off, it depends if you are talking about a point & shoot, or a DSLR…

http://electronics.howstuffworks.com/cameras-photography/digital/digital-camera.htm

I assume you want the basics;
Film and digital photography is broadly the same idea to start with;
light ‘rays’ are focused (brought to sharp points) from distant objects, thru the lens, onto a receiving strip, situated close behind the back of the lens, inside the light-tight camera body.
The strip can be a film or a CMOS/CCD chip, which is a glorified transistor that picks up pin pricks of light.
Film is a strip of chemicals, which responds to pin-pricks of light. The film has a coating which receives light and chemically changes – later the chemical baths are used to develop it, to bring out the shades, colours, outlines, etc.
The digital sensor is charged up by the battery and the light is registered (in pin-pricks all over it) and the computer in the camera ‘maps’ all the results as a big file. The more pin-pricks, the better the resolution will be (more tones in the final picture, more colours, sharper more realistic images). Generally, that is, the more mega-pixels (pin pricks) the better though small sensors can have a problem with ‘noise’.
Noise in film is the clouding of chemicals which, in a big enlargement, we see as gritty ‘grain’, if they are severe they can spoil a shot unless it’s one of Robert Capa’s.
Noise in digital world gives unwanted signals (like a mis-tuned radio) which we see as blobs of unreal colours, fuzzy or jagged edges that should be straight, or just (usually blue) grittiness.
So, to the photographer, there is hardly any difference between film and digital capture, other than speed and convenience when related to transmission or storing on a PC or Mac.
Really cheap film and digital cameras (and most phones) have issues with focus accuracy, lens quality, tonal range, all resulting in unreal smudgy unsatisfactory results unless all we want is a tiny web picture on the PC screen.
=Wide open lenses (‘f’ numbers under f 2,8) using all of the glass area, very high receptor or film speeds, meaning very sensitive to light (such as equivalent to ISO 800 and above, so we can take pix in very poor lighting), result in more noise, grit (grain) and colour shift problems more or less the same in both film cameras and their digital cousins.

I’ll leave out blur due to slow shutter speeds, dodgy cheap lenses, badly made mass produced cameras that don’t have their lenses accurately in line or at the right distance from the receptor.

Even the lens coatings matter – digital receivers hate internal reflections even more than film, so the glasses have to be multi-coated with layers of exotic materials that are a quarter of the light wave-length in thickness; we are talking very expensive nano-thickness vacuum coating technologies here.

Enough of that, the camera manufacturer does all that design for you, and puts it into mass production.

Now here’s the rub; film or digital, the guy who makes a modern computation/design and production that gives pix that look like hi-fi has to charge you. Currently, any new camera and lens less than say £500 (UK) will not be able to give pix that can satisfactorily be printed out at A4 and above, unless you don’t care about quality. That last phrase is critical!
If you want to be published in Life, Time, Vogue then start your kit at the £ 25,000 level upwards. The work involved in making this stuff is fantastic.
Back in the real world;
Most amateurs want reasonable results where the picture quality doesn’t ruin the enjoyment of the picture; that can be done either film or digital for the £500 I mentioned.

Second Hand.
There are now many pro kits for film at knock down prices which will yield tops results and because they were highly priced pro cameras originally, will now stand amateur use with ease, maybe after a service.
With digital cameras, we’re faced with second hand being even better value (BIG depreciations) but as the inventions have moved so quickly, we will always get ‘second best’ if we go that route; a Canon 5D was a superb machine with ‘L’ lenses on it, but the processor inside (the computer) was limited; the latest one is miles better but of course is still full list price.

Food for thought, as in all Life, you have to find the most convenient cost-effective compromise. Suggest you look at established top photographers exhibitions and really look at the picture quality, decide where your quality tolerance level is with respect to their masterpieces, and consider your purchases accordingly.
Do not, however, get hung up with techno kit thrombosis