There are a number of things you can do in post processing, including using HDR or using blended exposures. I think it's likely that something like that has been done in the example you give, because there's going to be a lot of natural dynamic range in a scene which includes both the sun in the frame and the shaded side of a building with no apparent light source.

Most of these post-processing techniques work best if you have the image in RAW, and best of all if you actually have a bracketed series. If you just have a JPEG, it you have less flexibility to work.

But the easiest trick for dramatic skies is to use a polarizing filter. These allow only light of a certain orientation through. They're made so they rotate in place, so turn until it's aligned with the sun — you'll see the dramatic effect in the viewfinder.

Take a look at this series of questions about polarizing filters for more:

• In which situations should I use my circular polarizing filter?
• How does one use circular polarizers?
• How do I choose a polarizer?

and also What is the difference between a linear and a circular polarizer? on the issue of circular vs. linear (which, although the name may seem otherwise, has nothing to do with with whether the filter rotates or not).

You also have to watch the light, an done position of the sun. The low angle of the sunset is naturally impressive, while mid-day light is harsh and hard to work with. I think you might also find Why do breathtaking views turn into "boring" photos, and how can I do better? and the excellent answers there helpful.

In general, I see that you know that the secret to good photos isn't the camera brand or model. But it's also not about after-the-fact software effects. From this and a few of your previous questions, it seems like you have a lot of interest improving your photography. We can answer a lot of questions here, but I also have a book recommendation. There are a lot of technical books on the knobs and dials of photography, but I don't think that's what you need. Instead, take a look at Capturing Light: The Heart of Photography by Michael Freeman, or The Photographer's Eye and others in that series by the same author. These books emphasize mental process for making photographs, and if you have that, you can figure out the technical.