Its not that difficult, you just need a camera that do auto exposure bracketing, a tripod and some software. There’s a bunch of them, but I use PhotoMatix Pro which is available for both Windows and Mac.
Yeah, HDR is not that difficult to do. You don’t even need a tripod if you have a program like Photoshop which has auto-align tools that will accurately line up your hand-held exposures for you. The basic idea, simply, is to expose a shot exposed for the highlights, one for the shadows, and one for the midtones, (or even more, but -2 EV, 0 EV, and +2 EV compensation is a good starting point) into one picture and compress the dynamic range, so you have a lot more details in the deep shadows and highlights than you normally would.
Now, in my opinion, the more exaggerated forms of HDR are very gimmicky looking, especially the third example in the OP. That said, there are photographers like Dave Hill who use aggressive HDR in a stylistic manner that works.
Still, it’s fun to play around with, and you can use HDR in non-obvious ways to coax details out of deep shadows and clouds. I occasionally use it myself, but in a very understated manner.
I shoot everything raw, but you can do HDR with JPEGs well, too. RAW gives you more flexibility, and you can eke out a little more dynamic range with it with fewer exposures. Before Adobe Lightroom had built-in dodge and burn tools which worked on the raw data (rather than the converted bitmaps), I would often do a pseudo-HDR for photos with a lot of dynamic range in them. I would export an image exposure compensated for the highlights, one for the shadows, and one normal, and then combine them in Photoshop, using the highlight layer as my “burn” layer, and my shadow layer as my “dodge” layer.
That said, if you shoot three JPEGs the same way, with consistent white balancing between the three (or even more exposures), you can do the same thing quite effectively with JPEGs. In fact, that is how I would originally do it before I started shooting raw exclusively. Normally, for me, it was an issue of eking out sky detail, so I would shoot one exposure for the subject, one for the sky, and combine the two in Photoshop, layering the images and using the sky exposure to bring out detail there in the same sort of way you would burn in the darkroom.