1. If you have not already done so, download and install GIMP. As of this writing, the latest version is 2.8, and it is available at the URL http://www.gimp.org/downloads/.
2. Create the frames of your animation as image files, in any file format that GIMP recognizes (for example, .gif, .jpg, or .png). Place all the images in a single directory, and name each file with a common prefix and a numeric suffix so that they sort in the correct order (for example, “Frame01.png”, “Frame02.png”, “Frame03.png” and so on).
3. Start GIMP, and wait for it to finish loading. If desired, enable single-window mode by selecting the item “Windows – Single-Window Mode” from the main menu bar.
4. In GIMP, select the item “File – Open as Layers” from the main menu. In the “Open Image” dialog that appears, navigate to the directory that contains the image files for the animation’s frames. If necessary, click the “Name” column header on the list box to sort the files in the correct order. [In the original version of this post, the user was instructed to sort the files in descending order, but it now appears that this advice might have been incorrect.] Then select all the image files in the list box and and click the “Open” button. The Open Image dialog will disappear, control will return to the main GIMP window, and each loaded image file will be displayed as a layer in the “Layers” pane.
5. Select the item “Filters – Animation – Optimize (for GIF)” from the main menu. The layers in the Layers pane will be renamed and prepared for export as an animated GIF.
6. Select the item “Image – Mode – Indexed” from the main menu. In the “Indexed Color Conversion” dialog that appears, click the “Generate optimum palette” radio button, enter the value “255” in the “Maximum number of colors” box, and select the value “None” in the “Color dithering” box. Then click the “Convert” button. The dialog will disappear and control will return to the main window.
7. Select the item “File – Export…” from the main menu. On the “Export Image” dialog that appears, select the value “GIF image (*.gif)” in the file format select box, enter the desired name in the “Name” box, and click the “Export” button. Another dialog will appear, this one titled “Export Image as GIF”. Activate the “As animation” check box, modify any other settings as desired, then click the “Export” button. The images will be saved as frames of an animated GIF file.