To bore a 2-inch hole through wood, you need a hole saw. A hole saw is a circular cutting bit that fits onto a drill. It has a pilot bit that initialises the cut and stabilises it while the cutting edge bores the hole. Hole saws are used any time a large-diameter hole is needed in any kind of wood project. The technique for boring holes through wood is exactly the same for any thickness of wood. You will need a 3/8-inch drill for wood up to 1 inch thick. For any wood over 1 inch, you will need a 1/2-inch drill.
Select the location you wish to bore the hole and mark it. Using the drill and the 3/16 bit, drill down through the wood on the mark. Make sure you drill as close to perpendicular as possible. If you angle your pilot hole, your hole saw will bind in the wood.
Remove the drill bit and insert the hole saw into the drill. Place the tip of the pilot bit into the 3/16 hole you just drilled.
Hang onto the drill with both hands. Turn it on and begin drilling, using the pilot hole to guide the hole saw. Take extra care to keep the hole saw and the drill perfectly perpendicular. When the cutting edge of the hole saw begins to cut, hang on tight.
Ease the cutting bit deeper into the wood, letting the teeth cut as you apply pressure to the back of the drill. Lean over the drill as you bore down. Continue looking at the angle of your drill to keep it straight. The hole saw should move smoothly through the wood without binding. If the hole saw binds, you may be angling the bit. Stop, check your angle and proceed drilling.
Ease off the pressure when the hole saw is within approximately 1/8-inch of penetrating the wood. Gently rock the drill slightly as you keep drilling. When the hole saw penetrates the wood, go as slowly as you can to prevent chipping. When the cutting edge of the hole saw starts to cut through, don't force it. Rock the drill around the circle slowly. Pull up on the drill, and break the few remaining fibres of wood in an upward motion to prevent chipping out the back.
Pull up on the drill while it is still running slowly. Pull the hole saw back out of the hole. Tap on the hole saw with the back of a screwdriver to drop out the plug that will remain in the hole saw body.
Always use both hands when boring large holes in wood. Large diameter drill bits and hole saws can bind, causing the drill to kick. Always wear safety glasses when working with wood.