Common sense and responsibility go a long way. Greyhounds have spent their lives in the company of other Greyhounds. They are pack animals and usually do well with other dogs. They are a sighthound and can see up to a half a mile clearly. They will be happy to chase cats, squirrels, or any other moving object, with or without your approval.
Greyhounds are true athletes.
They have been bred for speed. They have half the amount of body fat than other breeds. You should feed a high quality dry dog food, such as Iams, Nutro, or Pro-Plan. You should not feed grocery store brands, and stay away from food and treats with dyes. You can add vegetables or pasta occasionally, but don't over do it with table scraps.