Being the leader of your pack is important. As well as communication, socialization and being consistent.
Italian Greyhounds can be little manipulators. And are also intelligent, learn quickly, and they can be capable of extreme manipulation. They are very sensitive and do not do well with yelling, loud noises, and angry emotions.
Socializing must be started immediately. Introduce your puppy to new environments, new people, and other pets. Your puppy needs to learn that new people and things are exciting and fun. This is an excellent time to teach your puppy to walk on a lead. I like a harness for puppies, so they don't pull and choke. Later you can transition to a hound lead. It is essential that you give lots of praise and treats when learning to walk on the leash. Some puppies respond well to squeak toys.
Petsmart and Petco have puppy classes. Teach your puppy basic commands making it fun. He needs to be able to know at least Come, Sit, Stay and Leave it.
Get your puppies attention. Say "watch me" give immediate rewards for the desired behavior. Along with Lots of praise and treats.
Important: Points for training.
Communication: learn the subtle way your puppy is trying to talk to you. They will exhibit body language. Some will bark, whine, make other noises. My first Italian Greyhound would shake her ears making a noise when she needed to go outside.
Teaching acceptance of nail care. Begin by rubbing the puppy's feet and playing with their toes. I start clipping the puppies nails at 2 weeks. I introduce them to a Dremel tool that safely grinds the nails. I start by turning it on allowing them to hear the loud noise. I keep doing this several times a week. Then I start letting them feel the vibration of the Dremel. This is to desensitize the puppy so he will not be fearful. The next step is to do a couple of nails giving praise and treats, at the end of every step of training you must make it fun. Then gradually build up to doing all of his nails. Even if the puppy doesn't need his nails done. I touch them quickly with the Dremel several times a week.
This IG Puppy is very social. Has been trained well to walk on a lead, greet people and dogs.