Training and intelligence
They are fairly easily trained in that they are willing and want to please. However, this breed is a sighthound, and is very visually motivated, so a Greyhound gets distracted by movement. A reliable recall is hard to establish, and smaller dogs and other small animals will probably be persued.
Greyhounds, despite their athletic appearance, are calm gentle dogs. They enjoy socialising with people and dogs, but tend to present thelselves for you to appreciate them, rather than indulging in the dashing around of other breeds.
Attitude towards strange dogs and people
With strangers the Greyhound is aloof. This usually manifests in an attitude of, "You may approach and adore me, but I'm not that interested in you!" They generally are too laid back to make good watch dogs.
Grooming and shedding
The short, thin coat is very easily cared for with a once a week grooming. Greyhounds don't shed very much at all.
Contrary to appearances Greyhounds do not need vast amounts of exercise. They can run fast, but in short bursts, and they are then happy to relax at home. A couple of shorter walks a day will allow them to vent their energy in bursts as suits them.
Need for company
They do not enjoy being left alone too long - ideally Greyhounds like company to lounge around with.
Greyhound owners will need to have good boundary fencing, because this long legged breed can jump. They can run very fast, but are sprinters not marathion runners, and appreciate the opportuntiy to catch up on their sleep. This is a very tolerant, calm breed.