a trick of the trade, take a die grinder and cut the existing bolt flush, normally when a bolt breaks off it isnt flush and will cause the drill bit to "walk"
if you cut it off flush you will have a smooth surface to cut into, also go out and buy yourself a spring loaded center punch, they are like 2 dollars, use it to create a center point for your drill bit to bite into.

also use a very small drill bit first, work your way up, its better to start small, use cutting oil and slow speed
also have a magnet handy, bolts and their shavings are magnetic, but the case isnt so you will pick up all the loose shavings with the magnet, and not lose them down into the engine

thats all I will tell ya, for as much as I cant stand ya, would rather you do it right the first time than screw up anymore