Positive reinforcement is the best way of training any breed of dogs. This works well in the case of greyhounds too. They are sensitive dogs and don't respond well to harsh and punitive measures. In fact, they respond well to only positive methods packed with lots of rewards and praises. You can reward them either with treats or with verbal praises as well. While giving verbal praises, you should speak in a high-pitched energized voice. Give commands in a confident manner and don't confuse your dog with multiple commands for the same action.
If your greyhound does not obey you and comes up with some bad behaviors, immediately reprimand it by saying "No" in a low-pitched voice and ignoring him for a while. But if you hit him to correct his mistakes, then it will just create aggression in him. As dogs can also read the facial expressions, smile back when they do some tasks correctly or obey you. Use treats frequently to motivate your greyhound and to promote good behaviors in him.
Don't use a metal choker to leash your Greyhound as it may damage their throat while pulling it. Instead use a nylon choker or your safety collar. Never pull your Greyhound by the neck. Due to their thin body structure, they are prone to neck injuries when you pull down their choke or collar harshly. The most important fact you must know is that these dogs don't like to sit as their well-developed muscles and long backs make this a painful position for them.
As Greyhounds are scent hounds, they may not obey your commands when they smell something unusual that they would love to track. Sometimes they may even get off the leash to chase something. So, it's a wise idea to get a whistle and do some whistle training for "Come Back" response. It is also important that greyhound training should be done in an enclosed area from where they couldn't escape even if they want to. Always remember to give your Greyhounds a lot of treats when they accomplish the given task.