To sharpen drill bits properly by hand, you need a steady grinding wheel. Your average garage does not have one. Despite diamond dressing the wheels, I've rejected multiple new brand name grinders from HF to B&D to Delta for too much oscillation. The Delta vibrated just as much with the grinding wheels removed, so that tells you something. Just recently I scored a used Baldor 1/3HP and now I have something that I can use to sharpen by hand.
In the mean time, meaning the past 15 years, I've been sharpening bits using a first-gen DD 500. It has a chuck for LH bits, and instructions on tight twist bits, 2 things that many people think a Drill Doctor just cannot do. The 500 is not a gimmick, some of the lesser models are very limited though, some don't do split points or more than one angle.
Funny thing, the DD taught me how to hand sharpen drill bits. In order to function, the dull drill bit must first approximate the shape of a factory drill bit. Meaning, if it's broken off you'll never completely sharpen it on the DD. Because of oscillating mass-produced grinders I couldn't get a finished product off of a grinding wheel, but I could get it close enough the DD would quickly finish the job... perfectly.