Cutting precise, large-diameter holes with a power drill or cordless drill can be done with a variety of drill bit attachments, including a hole saw, spade bit, or Forstner bit. While each one has it's advantages, the Forstner typically drills the cleanest holes. But Forstner bits can also be tricky to use in a hand-operated drill, as they're better suited for use in a drill press. When used in a hand-operated drill, a Forstner bit has a tendency to "walk" away from the center, particularly if the tip of the bit is somewhat worn down.
There is a simple way to combat this problem. Create a guide for your bit by first drilling a hole through a piece a scrap lumber, using your Forstner bit. On this scrap, it won't matter if the bit walks at the beginning because once the main cutters engage the wood, the bit will begin to cut cleanly.
Then, clamp this guide board over the wood you want to drill and use it as a template for your Forstner bit. The scrap template will hold the bit in place and prevent it from walking across the finished workpiece as you cut down into it.