Could someone give me the low down on how to take shots like

>>3115707
Larger aperture. 1/500 or higher shutter and slightly underexposed.

>>3115707
Expose for the flames, raise the black point in post. Take off some saturation, give back the saturation to yellows, orange and reds.

Thanks guys! Keep the suggestions coming :)

>>3115707
these
>>3115712
>>3115714
And you can make this with all the entry level model DSLRs and kit lens. Not such a thin depth of field, but on the long end (55mm) it will have a decent separation.
This is essentially a portrait shot. A portrait of a fire, not a person but a portrait so the rules for portrait shots apply here as well, or using this method you can take decent portraits of people.