The quickest and easiest (although not 100% accurate) way is to go to a gas station or office supply store and pick up a copy of an ADC map of the area -- I particularly like the "Metro Atlanta" map, whic is $19.95.
It shows areas inside city limits in yellow and unincorporated areas in white. If you see areas that appear to be right on the line between an incorporated area and an unincorporated area, then you'd do well to research further using the links LMM provided above, but if you just want to get a feel for which neighborhoods are Atlanta and which are DeKalb, this map is super helpful.
Good luck!
