Step 1: Take Pictures
As I'll show later on, having a steady hand is marginally important; just try to get the same general area in every shot. My technique in this particular case was to point the camera in such a way that the viewscreen showed the exact same object in the corner -- a small garden decoration -- in each shot.
Take as many as you like, until your arm gets tired, or until your camera runs out of memory! For this example, eleven shots will suffice. Make sure the shots are evenly timed, as good as you can. The more evenly-spaced they are, the smoother your animation will look in the end. For fast clouds, like here, I spaced the shots 2-3 seconds apart. For slow clouds, 5-10 seconds is better.
Step 2: Put the pictures on your computer
In my case, my pictures were located on a memory card in my cell phone, which is what I used to take the pictures. I put the memory card in an adapter and plugged it into my laptop as a flash drive. Other devices will probably be more cooperative for you; most digital cameras utilize a simple cable to connect, or even transfer files wirelessly.
Save the pertinent pictures in their own folder. Make sure to keep them in the order in which they were captured. Some cameras have ridiculous naming conventions for the files they create, so this may be difficult. Windows does a pretty good job of sorting them properly if you select the "modified" option under "arrange icons by..."