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Two tools will be useful for adding signatures. The icons and descriptions are below.
Using the previously rendered sphere on checkered plane (source here), open the rendered output in the GIMP. Do this by File->Open or Ctrl-O and select the rendered output image. GIMP should pop up a window with the image in it like the one shown below.
Add text to the image: this will be used to add the signature text
Move layers and selections: this will be used to position the signature on the image
From here, select the signature font. Do this by clicking on the box to the right of 'Font:' in the Tool options. This tutorial uses the 'Embargo' font. After finding a satisfactory font, the color needs to be adjusted. Click on the box to the right of 'Color:'. This will pop-up the Text Color window.
Select a shade of gray. 25% - 33% gray (meaning, it's 25% - 33% of white) works well. This can be done by manipulating the 'V' (value) slider to 25, or setting the 'R' (red), 'G' (green), and 'B' (blue) sliders to 64. Note that the red, green, and blue sliders have a range of 0 - 255, so 25% is about 64. After getting the color set, click 'OK'.
As the signature text is entered, it should appear over the image as shown below. If the text position needs some adjusting, use the 'Move layers and selections' tool to relocate the text. Once the tool is activated, left-click on the text and drag it to a preferred location. Be careful to click on one of the letters and not the background. Its easy to accidently click the rendered image and rearrange it instead. If anything goes awry, Ctrl-Z is the undo command.
There are many other effects available, including Subtraction, Multiply, and Divide. Spend a little time trying others to see how it changes the signature. After the signature is complete, it can be saved via File->Save, File->Save As, or File->Save Copy from the image window. Behold, the signed rendering: