Technique of making an impressive fire image is very simple. Firstly, you should take a photograph.An easy way to do that is to go to a family picnic. Use an "A" (aperture) mode and set the aperture setting from f/5,6 to f/11. When you're using this values, you will take really good sharp images. Then set exposure compensation to -1 EV due to have a dark background. I recommend to use telephoto lens, because you can use it away from bonfire and your equipment will be intact. The best way to have good final image is to shoot in raw.
The second step is postprocessing. In Photoshop your raw image firstly opens in Camera Raw module. The main option here is Blacks. Set it to 40 or higher to make background almost black. Also you can use temperarture to change hue of the flames.
(above you see settings, which I'm using in 90% of firey images)
To complete this postprocessing you can darken the background using Burn Tool and increase contrast using Curves or Levels. And it's done!