Greyhounds are dogs that can be very well socialized to be around people even though by nature they are timid. You will want to either socialize your dog while it is still young or, if adopting a race dog, you will want to try and adopt one with a friendly temperament that seems intelligent enough for further socialization.
As a puppy, a greyhound can be taught to enjoy being around your family much more easily than as an adult. While a reserved breed that can be startled easily, it is not prone to aggression. You probably won't have much trouble with it trying to intimidate strangers, you may have more problems with it running away and hiding. If you have other pets or are considering more than one dog, you will want to get them around the same time so they can get accustomed to each other. Greyhounds like to chase anything that looks like prey to them, so if the household animals, like cats, are made familiar with the dog before it is full-grown, then they can become the best of buddies.
Greyhounds can have an independent streak to them. If you want to get obedience training, you should do it early. This will help them to be mindful of your property and obey some of your commands. The dog may be highly intelligent, but it is easily distracted, and this can influence exactly how obedient it appears to be. It is a graceful dog and isn't prone to disturbing lamps and furniture like other big dogs.
If you adopt a greyhound, the dog will be more mature. It will also probably have been somewhat socialized into accepting the presence of strangers. It will have been handled by a variety of trainers, so it won't be too hard to expand those socialization skills to its new home. You will want to have a good routine set up for the greyhound, so it knows what to expect and can settle into its new life with a minimum of disturbance. If they need further house-training, start by crating them again and letting them loose for exercise and in appropriate training areas. As prior race dogs, they will be used to the crate and may even find it comforting in a new environment. Try to keep its environment quiet and calm, with some activity. Once an ex-race greyhound is socialized it will take to its new role as couch potatoes with gusto. You may even be surprised that such an active dog on the racetrack loves to lie around the house and enjoy its retirement and its new family life. A socialized greyhound makes an ideal pet and many of them become very friendly and warm towards their new adoptive families.