Martingale collars (also called limited-slip collars) are usually made of flat nylon with a smaller fixed-length section (made of either nylon or a short length of chain) that, when pulled on by the leash, shortens up tightening the collar around the dog's neck, to a limited extent. When properly fitted, martingales are looser than flat-buckle collars when not tightened, and less severely corrective than slip collars when tightened.
Most training schools are happy to allow you to attend and observe (leave Fido at home for this) a class or two to be sure the style of instruction fits with your beliefs. Dogs learn best through progressive reinforcement training; rewarding the dog for making the right choice and withholding rewards, or ignoring the dog for making an incorrect choice.

I felt that Hilton was able to apply various protocols to meet my dog’s needs due to his extensive background with K-9 training in the military, police, and service dog environments. Hilton demonstrates a firm hand while training, but uses positive reinforcement as well, which was needed for my dog. He ensures that you know the protocols to carry over in the home environment after training is complete. If there was any question regarding Auggie’s behaviors at home, Hilton was available by email, phone, and even conducted follow up sessions at my house.
Head halters are an alternative to collars that works similarly to a horse halter. The halter fits over the dog's snout and behind its head (leading it to sometimes be mistaken for a muzzle). Halters reduce the dog's ability to successfully pull on the leash, but do not eliminate it. If the halter is used with a sharp jerk on the leash, neck injury to the dog may result, but used correctly head halters have not been shown to cause harm.
Unless you plan to keep your dog outdoors--and few of us do because it's not recommended--you'll need to teach your dog where to eliminate. Therefore, house training (also called housebreaking or potty training) is one of the first things you need to work on with your dog. Crate training can be a very helpful part of the training process. This includes house training as well as many other areas of training: