Try with simple things like a camera pan. I learned Blender in this way. I think Terragen 2 uses key frames. Start with the camera pointing at one area of the landscape. Make a keyframe. Set the time/image to maybe 100. Rotate the camera a little, 40 degrees maybe. Create a second keyframe for frame 100. Make a new directory to store the images. Set the output to this directory.
Just use the default start landscape without shaders. Use quick render at 320 x 240 resolution. Even my computer can calculate the frames pretty fast with the default shader. You should see a series of images start to appear in the save directory.
When it's done, set up the animation record for the number of images and the number of images in the directory. In Blender, you would use record sequence. You should have a simple animation.
I have never used the animation features of Terragen 2. I don't think the free version allows it, so this is a guess of how to do an animation using Terragen 2. Most program use a method similar to this.