Animated fire tutorial Part I: starting from scratch
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Difficulty:
easy 
Time:
several minutes
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Step 1: Let's start this tutorial by making image with the black background, size doesn't matter.
Step 2: Now create another layer with the rectangular marquee tool and colour it white, usually it should be 1/5 of the whole image height.
Step 3: Apply this filter: go to Filter > Blur > Guassian Blur and enter around 10 - 15 px.
Step 4: Duplicate the layers. 4 or 5 times is suggested for a clean animation.
Step 5: Select the Smudge tool in your toolbox. In case you don't know how it looks, check the image.
Step 6: Use the smudge tool to smudge the white blur layer. You do this by clicking and draging from the bottom up.
Step 7: Repeat the above thing through the whole image.
Step 8: Repeat step 6-7 on all the layers. Then just simple create each frame for the each layer you have aka basic animation
. At the end, just throw some colour and you should get something like this:
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Part II:
Using the above tutorial on signatures with a non animated fire