Mark the center where you will drill the hole for the dowel. Insert the 1/8-inch drill bit into the chuck of the electric drill. Drill a 1/8-inch hole straight down into the material, making sure that you center the drill on the mark. Remove the 1/8-inch bit from the drill.
Insert the hole saw arbor into the chuck of the electric drill. Slide the hole saw over the arbor and tighten the chuck until it is secure. The drill bit in the arbor should project past the tips of the hole saw's teeth by about 3/8 inch. This won't be an issue unless you are using an adjustable arbor, as hole-saw kits with fixed arbors will always include the right-sized arbors.
Start the drill going slowly and slide the tip of the bit into the 1/8-inch hole. Use this hole to guide the hole saw straight into the material. Apply steady pressure and increase the speed of the drill. If you are making a hole in wood, back the hole saw out from time to time to clear sawdust from the cut. When the saw breaks through, back it completely out of the material you are cutting before letting go of the trigger.