The best way to socialize a new puppy or kitten is to expose them to a variety of people, animals, environments, and experiences in a positive and controlled manner. This can include introducing them to different sounds, textures, smells, and sights, as well as other pets and people of varying ages and backgrounds. Additionally, providing plenty of positive reinforcement, rewards, and training can help them feel confident and secure in new situations. It's important to start socializing them early in their development to help prevent behavior problems and fears later on.