Nellana is right about ONE thing. ALL dogs can be trained with 1 method...just not hers.
Dog training is pure common sense. I teach behaviors with food and toys. That way I'm teaching that there IS indeed something in it for him. Once he understands the commands I correct him for not performing them when commanded. Later I correct him for performing them as commanded but not 100% perfect, for example my dog breaking eye contact while heeling. Then I add distractions and correct the dog for falling for distraction.
ALL that time I STILL give positive reward. I STILL give food. I STILL give toys. There is always something in it for the dog. People talk about weaning dogs off of food and toy rewards after they know commands. So how would you like it if I hired you, taught you how to do your job correctly, then weaned you off your paycheck? When one uses common sense and thinks of it this way it sounds a little silly doesn't it?
I do make the dog work for longer periods before reward, but reward is a constant.
Now the huge sweeping statement about this method of training works for all dogs is true if you keep this in mind. No 2 dogs are the same, if you have a soft dog who doesn't take correction well then obviously you tone down and tailor the corrections to it's temperament.
If you have a hard dog who takes hellacious corrections then you tone them up and tailor the corrections to it's temperament.
If you have a dog who isn't motivated very well by food, you use toys. If the dog is not interested in toys, but "overly" interested in food reward to the point it can't focus, you use a treat of lesser value to the dog (something he doesn't find as the best food in the world which can be bland treats or even kibble). If your dog is a slow learner you spend more time with the 100% positive teaching part of training. If you have a quick learning dog with a hard temperament, he can be moved along through training faster.
You can train ANY dog on the PLANET no matter how highly motivated, no matter how apathetic, no matter what breed or size with this method. Teach with positive methods, correct when you must, and proof around distraction. I've trained every dog I've ever had my hands on this way, Search & Rescue, dual purpose police K9, narc dogs, explosives detection, Schutzhund, IPO, PSA, French Ring, trailing dogs, catch dogs, hounds, my rescue American Pit Bull Terrier, 6 week old puppies, 15 year old dogs, German Shepherds, Rottweilers, Retrievers, APBTs, a mini Dachshund and my little Chihuahua/Jack Russell Terrier mix and dogs from every temperament from dangerously hard to dangerous fear biters and all the happy "normal" dogs in between.
Every dog can and should be trained with positive reward. And every dog at some point in it's life it WILL need a correction.