Step 1: Create a New Document
Once you have your document, create a new layer. Using a small brush, draw some form of flame using red.
Step 2: Create the Second Layer
Now fill the selection with a deep orange using the paint bucket. Invert the selection (Shift+ctrl+I) and press delete to rid yourself of the red in the layer.
Repeat this process to create a yellow layer within the orange one.
Hopefully, you are left with one very nasty looking flame that appears to be cut from several layers of paper. Not to worry!! Easily remedied.
Step 3: Blur
Move on to the orange. Do the same Filters>gaussian blur trick, but decrease the radius a little this time.
Moving on to the yellow, decrease the radius even more.
Hopefully, your flame looks slightly less atrocious now.
Step 4: Brighten Your Flame
Duplicate all of the flame layers and merge the duplicates and the originals seperately. This ought to give you two perfect flames. Choose the one on top, and bring up the Hue/Saturation panel (Ctrl+U). Drag the top slider 'till the thing turns an odd shade of bluish purple. Move the slightly discolored layer to behind the original. Change the original's blending mode to "soft light" and merge the two. Duplicate twice. Change the middle layer to orange using Hue/saturation (click the "colorise" box), and the top to yellow. Set the blending mode of the top two layers to "color dodge". Copy all layers without the background, and paste. Now hit Ctrl+F to apply gaussian blur. Voila! your charmingly simple, somewhat realistic photoshop flame!