According to Gardeningtipsnideas.com, you should cut the branches off the existing bush at the end of the summer. If you wait too long, you will have little success growing your plants because you don't want the buds to open too quickly (which they will do if you catch them too close to the end of their dormancy and the start of their growing period). Cutting the branches early in the dormancy period of the bush will net the best results.
Use rooting hormone powder. Apply this to the cuttings and store them in a bag in your refrigerator until spring, when you can plant the cuttings. This step is not absolutely necessary, but it will give you a far greater chance of success when you plant the blueberry cuttings later on.
Prepare your soil. Blueberry bushes prefer acidic soil with a pH level of 4.5 or 5.0, so make sure you test your soil with a soil testing kit (you can purchase one wherever garden supplies are sold). Add the required amount of fertilizer to bring your soil to the proper acidity before planting your blueberry bush.
Plant the cuttings. Place the cuttings into your acidic soil in the early spring, and water and fertilize regularly. In a few seasons you will have a successful, thriving blueberry bush that you planted from the cuttings of another bush.