Any time you have a visible, compact light source and something solely illuminated by that light source in the frame but slightly away from that source, that will overwhelm the camera's sensors. You will not be able to properly expose the subject (the thing being lit) and the light source at the same time. The reason is simple physics. If a particular 1-square-inch point is emitting 100 units of light at both the camera and the subject, that light dissipates as the square of the distance. So ten inches away, only 1 unit of light is hitting a one-inch-square portion of the subject's face, and only a fraction of that is actually reflected. That maximal 100:1 ratio of light is already going to be very hard to expose for; if your subject is instead three feet away (36 inches), you will instead have a 1296:1 ratio of light between the bulb and the subject's face if your camera is equally far from each (which is necessary if you want to use selective focus without a tilt/shift lens and want the source and subject to both be sharp focus as in the example).
The ways around this are fairly well described in the answer by Caleb, although a "dimmer bulb" is not going to help (still the same ratio in effect, you just will have a longer exposure to get it).
I would generally either exclude the light source somehow, shade it from the camera (an ND filter although that may have too-obvious artificial effects, or adjust the shade on the lamp, or as Caleb suggests last wrap the camera-facing side of the bulb in a gel to reduce how much light it sends to the camera, or put a gauze curtain up if you are okay changing the composition as in a portrait session), or make it an interesting reverse-silhouette. The example works well not because the flame is properly exposed, but because the candle flame is an interesting enough shape to stand in frame without distracting (and the judicious use of selective focus, eyes, and contrast on the right side of the frame absolutely help in keeping the eye from wandering far). You might get a similar effect from a clear bulb with an interesting filament arrangement.
Having a "fill" light is a little more advanced (and to my eye the shadows in the example appear to show that a shaped fill light was used, although I might be overanalyzing it). The important thing is that the fill light needs to match the temperature of the light source - a daylight flash, even soft-boxed, will destroy the soft yellow glow of an incandescent or flame. It also needs to affect the subject without affecting the rest of the scene, and also not reveal a harsh transition between the fill light and the portrait light.
In the example, I believe that a fill light was used, just off to the left and slightly elevated out of frame. The "fill" light is essentially hitting the subject at the same angle as the candle flame (although the mismatch is evident in the child's arm which seems overly-lit for a candle light alone).
Compositing tricks can also be used. HDR is one of these, but you could also try frame-stacking. I'd always prefer an in-camera effect to post-processing, though; generally such photos turn out more real-looking than post-processed. Still, you can get a good realistic look using HDR, if done correctly and without a bunch of "local contrast" applied.
