Greyhounds— whether you bought them as puppies or adopted them as full-grown hounds— should be trained upon arrival at your house. They can be stubborn and will tend to think about what they will get as a return when they follow you during training sessions. Overall, these independent pups should live with confident and consistent owners. They're sensitive, too, and harsh training won't work. Consistency, patience, and rewards-based training methods (especially food rewards) are the ways to go. Never resort to punishments.
Greyhounds may find it difficult to follow your "sit" command. These dogs don't naturally sit, and they may even seem as though they're balancing on the tail.
Socialization is essential. Expose your hound to various situations so that they won't grow up timid/fearful. You may try socialization classes offered in obedience schools, in which your Greyhound can also get started on the basics of obedience.