Choose a subject. This can be done in one of several ways, either you will need to find a picture of flames online, or you will need to take your own pictures. Choose a subject to study and paint from, in order to make the flames as realistic as possible.
Sketch the flames (or flame) on the canvas or paper before painting. Sketch lightly and do not worry about details. Keep in mind it is easiest to paint flames against a dark background. In daylight, most fires and flames will be less noticeable to the viewer. Thus, most of the area around the candle will be shrouded in darkness.
Paint a light wash of the background color(s) around the flame. Leave a buffer space between the flame and the background color.
In the buffer space, paint a light wash of a soft orange/yellow. Overlap the light wash with the shadows in the background and allow the color to fade as it draws near to the center of the flame.
Build color in and around the flame in repeated layers. If you are painting a larger flame like a hearth fire, the flames will be more visibly orange and yellow. Allow the darker colors (shades of orange) to line the outside of the flame and the brighter, lighter colors (shades of bright, intense yellow) to reside in the flame's core. If you are painting a candle, the flame will be intense and nearly colorless, and there will be only faint color around the exterior of the flame.