To take a photograph, to capture an image, is to freeze time. More specifically it is to capture light. Space and time are intrinsically linked, but theories of relativity are logically independent of any properties of light, unlike photography. To record an image using a digital camera, reflected photons must fall onto a sensor, where they are recorded at a pixel-level. The more photons there are per pixel, the higher the signal:noise ratio, and the cleaner the picture. A 16MP camera might have JPEG options for 4MP, 8MP, 16MP and RAW + JPEG. Which is best? The numbered JPEGs are picture files which have already been processed by the camera itself. They are good to go, are small in size, and contain limited information (i.e. little more than you can see). The best option, in terms of image information, is to shoot RAW + JPEG. That way, you have a decent JPEG you can email, upload to FaceBook, Google+, but also a relatively huge RAW file containing oodles of information about that instant in time you just captured.
A friend at work commented that he's considering taking some photos in RAW and having a look at convertor software such as Adobe Lightroom. I've written about this in some detail before, but it's a topic which comes up so often as to warrant revisiting. In fact, from that previous post, is the following closing statement:
So, keep snapping away. If you're wondering whether you should be using RAW or JPEG, just use RAW+JPEG. Computational storage space is not expensive, so go ahead. However, out of camera (OOC) JPEG files are rather good these days, from all manufacturers. Time spent working on ideas and composition is more valuable than time spent worrying about file formats and sensor sizes.
I'm pleased to say that I still stand by those remarks. RAW + JPEG is a good way to shoot if you're not sure which to shoot—you can always bin the RAW later. Sticking to JPEG only, could just leave you with a few "what if" feelings...
I shoot RAW only, and have done since getting my first digital camera back in 2007. That was a Canon 400D, which I bought with the express purpose of documenting fieldwork in Borneo. The dynamic range of digital sensors has improved immensely in the last 7 years, to the point where the tiny little RX100 quite frankly embarrasses many DSLRs—even some of those made today. We're at a time where ISO ratings are almost meaningless; they are at least decoupled from their original meanings and relations in the film era. Shooting in RAW allows you to bring the darkroom to your living room.
You want to get the most from your photos. You capture the best possible image you can at the time, and now you want to get the best possible results out of your files. My recommendation, would be to use Adobe Lightroom (LR). I used to swear by Apple's Aperture, but left it in 2010 after Apple let it stagnate and fall far, far behind. If you own a Mac and a camera from mid-2014 or earlier, do consider Aperture, as it's faster (mostly due to utilising the GPU and CPU, rather than Adobe LR only making use of the latter), and smidge cheaper. Adobe LR is updated much more frequently, and Adobe are very quick at getting the latest lens profiles (which allow for lens-specific software correction to optical characteristics). I also prefer the way LR works (it took a while to adjust, admittedly), and the fact it is OS independent (i.e. I can use it on Mac or Windows). There are other RAW convertors such as Capture One, which is free for owners of Sony cameras. If you have a Sony camera, it might be a fun place to start. I downloaded it, but couldn't really be bothered changing my workflow, and didn't see any benefit in output over Adobe LR anyway.
RAW files, after straight conversion, may look a little bland, a little raw. They are the raw information recorded by the sensor; a digital negative if you will. They need processing. The best thing, is that with most RAW convertors, you get non-destructive editing. This means that if you make changes to an image, you can undo them all. You can change everything black and white, undo it, or make a virtual copy and have both.
My RAW workflow is, in my opinion, relatively simple and straightforward. I import the photos (don't delete them from the card until they are backed up), usually apply a touch of contrast, a bit of sharpening (no noise reduction), lens profiles if they exist, and then consider moving curves. Curves are probably the most advanced procedural step through which I put my RAW files. I don't really have any formula, other than to only move any slider or curve by no more than about 25% (except sharpening, where I often apply as much as 60%). Moving sliders around will definitely create some surreal and dramatic looking images, but it's generally not my style. I prefer smooth tonal transitions and other subtleties. That doesn't mean that HDR (High Dynamic Range) photography isn't any more a valid art form than my work, or mobile phone pictures, it's just not really what I'm into.
My final advice would be to shoot in RAW and JPEG, and then try to see if you can edit the RAW to look like the JPEG. You can afford to be quite bold with the sliders—just see how things go, you can always undo it!