How to get that really cool sky affect with a camera?

Example:
or
The sky almost looks flat but it looks so cool: D
I have a nikon d5000 if that helps.

Those are taken using long exposures. I say long, what i mean is long enough for the clouds to move significantly during the time the shutter is open.

It's really easy to try it for yourself. Ideally you need a tripod, but if you don't have one you can rest the camera on something steady (steady enough that it won't move when you release the shutter). Then set the camera to shutter priority and experiment with different shutter speeds. Depending on the weather and how fast the clouds are moving, you may need a shorter or longer exposure. Depends what result you want. But go experiment, that's the best way you'll figure it out.

Both shots were taken using some kind of wide angle lens, maybe like the Nikkor 10-24 mm

The first one was a long exposure, maybe two to ten seconds (to do this you will need and filters so you do not overexpose the shot and experiment to get just the right amount of "cotton" effect of the sea)

The second is just a matter of waiting until the sun and clouds were just right before pressing the shutter release.

Make sure that you have your camera on a good sturdy tripod and that the camera is level to the horizon.

The first one was taken with a slow shutter speed, but the second wasn't. The second looks to me like the contrast was bolstered in a photo editer.
The main trick employed was good composition and patience. I can almost guarantee that the photographers didn't just happen upon these moments and say "that looks good, I better take a picture and see how that turns out". They took time to compose the shot, Found the right spot, waited for the clouds/sun/subject to be in the right place, made sure the horizon was not in the middle to encourage the eyes to wander over the picture, and they probably took more than one shot and picked the best one of each shot.