Though stone is trickier to drill than wood, the process is very similar. The real key is to understand what kind of stone it is. While most woods are of very similar texture, the hardness and durability of stone varies widely.
Learn all you can about the stone you're drilling into. Some stone (especially concrete) is easy to drill and very forgiving. Other stone (like limestone) is extremely brittle and hard to drill.
If you don't know yourself, consult with a hardware store about what kind of equipment you need to use with the stone in your wall. Some stone will require highly specialized, expensive equipment; others just need a regular drill with a harder bit.
Being certain to wear safety goggles, drill the hole in short bursts.
If you hit a particularly hard section of stone, don't try to power through it with the drill. Instead, insert the masonry nail and drive it through, using your hammer. Once you've broken up that stone, go in again with the drill.