After taking several pictures of clouds outside my home, I noticed that they were at very nearly the same direction. By viewing them in rapid succession, they almost looked like a frame-by-frame time-lapse animation. I decided to turn it into an animated .gif file to share with my friends and family. Here's how I did it!
Step 1: Take Pictures
Find something interesting but which changes or moves slowly -- in this case, the weather. I stood in my backyard and took several pictures of the same general area, while standing in the same place.
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.