See section on crate training, also, because using a crate is such a big part of this process (and it lists the equipment to get).

Dr. Dunbar has a very precise method of potty-training puppies. He says that in some ways, they are very easy to train, but they have very small bladders and can only hold their pee for a little over an hour. Thus, if you can bring your puppy outside every hour (on the hour), then the pup will never pee or poop inside. 

• What do you do at night? At night, puppies can hold their pee and poop for about 4 hours. So set your alarm for 4 hours into the night, then wake up, go wake up the pup, and lead the puppy outside to pee. (Note: Don't carry the puppy, but rather, insist that the puppy actually walks out with you).
• What do you do when you have to leave the house for more than an hour? Well, sometimes you may have to leave the puppy alone (although it's best to bring the puppy with you because then they can get more socialization). In this case, set up a fence around the crate (see this post, which is two blog pages of notes on Dunbar's potty training book, for details). In the area between the crate and the edge of the fence, put down a potty pad. That way, the puppy can pee in a "designated spot" rather than randomly peeing on your floor. Again, this method is only as a backup. Usually, you shouldn't be leaving your puppy alone for more than an hour (because you want to bring the puppy outside to pee every hour, thus never letting the puppy pee inside).

With this method, theoretically, the puppy will never pee or poop indoors, and thus the puppy will never be reinforced for pottying indoors (thus leading to a much faster potty-training time). This way, you are "setting the puppy up for success." After all, why set up a situation where the puppy would ever pee indoors? If he/she pees indoors at all, they will take that much longer to be potty trained.

• What if you take the puppy outside but they do not pee or poop? Give the dog three minutes (time it), and if they do not potty, then bring them indoors and put them in their crate for twenty minutes. Take the puppy out then, and then the pup should potty outdoors. Repeat as needed.
• What if the puppy does pee or poop indoors? Don't react, just clean it up, then clean it again with a product like Nature's Miracle or even vinegar-water (so the smell doesn't encourage the puppy to go there again).

After a couple of months, you can extend the time to 90 minutes, and then 2 hours, then 3 hours, etc., adding an hour each month.

Notes:

• Dr. Dunbar also talks a lot about proper socialization of puppies. I'm shocked at how his amazing emphasis on socializing puppies isn't more well-known (have them be held by 5 strangers a day, for the first month you have the puppy). If everyone used this protocol, 90% of dog problems would be solved.
• He also has a great method for crate-training a puppy.