The first thing you must have uppermost in your mind:
No matter what "crime" your dog may have committed, how long time he took to come when you called, or how worried and angry you got when you called in vain - you must ALWAYS show true love and a hearty warm greeting (preferably with a small treat or two) when the dog finally does come back to you. You may need to be a good actor/actress for this!
In other words: Your dog MUST be able to be sure of a warm and loving welcome AT ALL TIMES, no matter what he did prior to coming to you. He must learn from his earliest days, that to be by your side is the most pleasurable situation! He must know that you, without fail, are always glad to see him again. He must look forward to being with you again if, as and when he runs off - and he will!
Far too many owners make the fatal mistake of showing their quite natural anger and frustration when their dog has been disobedient or in some way let them down. They also feel the dog should be punished.
But it's impossible to explain to a dog that, whilst he did right here and NOW when he finally came when you called for the 100th time, he did wrong prior to this by delaying coming.
There's just no way you can explain this subtlety to any dog.
Punish him and be angry when he finally does come and next time you can be sure he'll put off the evil moment of rejoining you, perhaps even learn to dread coming, as next time as he knows this will only be unpleasant.
Never reproach a dog for being slow to return - he'll then only be even slower next time!
I have seen many a dog slinking along TRYING to come its angry owners, tail down and hating and scared of the situation and nervous of the scolding or maybe even blows that will ensue. I have seen hunters hit their dog when it was disobedient.
So do not ever fall into the trap of showing your negative emotions. Never punish a dog for finally doing the very thing that you have after all, been trying to get him to do for the last 10 minutes or more!!!

Photo: An Eikica show Greyhound posing beside a Danish lake in winter.
Training:
From the first moment you bring your new dog into your home, have some dry puppy food always at the ready in your pocket. (I say puppy food, as the pieces are very small - do NOT use something unhealthy like chocolate, which is poisonous for dogs! Rather use a brand of dog food that you reserve only for treats.)
Call his name in sweet (but commanding) tones and reward with praise and a single piece of the puppy food every time he comes. Do this often - but not so often he gets bored with it! This is the first important step. Takes just 5 minutes to learn!!!

The place where you will walk the dog
The next step is to choose with care the area where you will take the daily walk.
There must not be busy roads too near or too many wild animals. Open areas are best for Sighthounds as they CAN crash into trees - they look back to see what you're doing or if other dogs are chasing behind and at high speed, suddenly - wham!
Take the walk five or six times or more (if it's an older dog who's new to you, then MANY times over 2-3 weeks), whilst keeping the dog on the leash. (Once a day, not 5-6 times a day!) Let him examine the route the whole time.
The idea is that he learn the route thoroughly before getting his freedom. By learning the area, he won't get lost or panic if suddenly he runs off the beaten track. It's best to always take the same route each time.
Always walk at the same time every day.
Wild animals learn quickly and will scram out of it fast, prior to your coming each day - if they have a chance to get to know you! Fix something on to the dog's collars that rings or tinkles and the sound of this will act as a warning to all the wild creatures. A hare only has to be chased after once and it will make quite sure it doesn't happen again if it can recognize the same collar bells ringing! You can whistle, sing and speak unnaturally loudly to the dogs or stamp or clap occasionally - anything that will scare wild animals far away! Believe me, the wild animals soon learn to keep away from your dogs!

I'm of course assuming that you, as I do, have the dogs as pets living in your house together with you. For those of you who have their dogs shut away somewhere the most of the time or permanently, this close bonding between owner and dog is impossible and you may never be able to trust your dog in the same way when, if ever, it runs free. It will no doubt ignore you and make full use of the freedom and refuse to be caught. I know I would do the same, if I was a dog who never went on regular walks!

WARNING: If it's an older dog you've taken over from someone else, who is not used to having his freedom, take an extra long time getting him used to the area where you walk whilst keeping him on the leash, and be sure he has become devoted and faithful to you and comes enthusiastically every time he is called. I'd take several weeks to be on the safe side. I always train my dogs to come to a whistle as well. A soundless whistle carries further, especially for men whose voice is usually isn't as effective as a womans! A whistle can also be used by others, should they walk the dog for you one day - so he's not just used to just one or two particular human voices. And it's more discreet than plain standing hollering, should he disappear and other people are around!

Note: Never underestimate how different you may look to a dog when he sees you from a great distance - and maybe for the first time! Remember that moving objects are easier to spot than stationary, so don't just stand there calling, run to and fro! You can also wave a large white handkerchief. I always do. He will also tend to run to look for you where he last saw you - so don't wander too far away.

Two of my Whippets enjoying the cool lake waters on a hot summer morning walk. They hate to get wet and never swim, but "cool paws" can be a pleasure!

When out on the walk, it's important to occasionally call your dog to you and praise, love him and give a treat - and then just let him go again. This way, he'll never know the moment when you plan to "capture" him permanently and put him on the leash. Dogs CAN play up when they sense that the end of a walk is nigh - which is usually all too soon in their opinion! I have never had a sighthound who did this, but the possibility is there.
You can also occasionally walk on for 5 minutes and then release him again. He should get a relaxed attitude to being restrained on the leash - and a relaxed attitude about running free.
Dogs who rarely get the chance, cannot be blamed for playing up and trying to prolong the fun - much to the owners frustration. Such owners often swear: "never again!"
But one should rather take the dog for a daily run, give him time to get used to the situation and enjoy it like it's no more special than his dinner each day. A dog who runs free every day, will always be attentive to his owners wishes - and happy and well balanced in himself. (And a good mover at shows!) He'll find running free no big deal and will always be willing to come to you again. You will get a lot of pleasure from seeing him run around. Sighthounds are simply beautiful in motion and you can see all their muscles flexing!