Qualifications: I'm the father of two girls. I trained them both using this method. One was very quick, the other took some extra time.

Origins: We followed principles found in "Toilet Training in Less Than a Day" by Nathan H. Azrin, PH.D. and Richard M. Foxx, PH.D.

http://www.amazon.com/Toilet-Training-Less-Than-Day/dp/0671693808/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1216383896&sr=8-1

If you like this approach, buy the book (or get it from your library). It includes some important details that I've glossed over here.

This method emphasizes teaching the child to do the whole process by himself. It's important that he can just get up and go when he wants, without having to track down an adult to help him.

Step 1: Materials

You will need:

A child

Your child should be old enough and possess certain skills. More on that in the next step.

A potty chair

The collection bucket should be very easy to remove from the top. It should not stick or require sliding in from the back.

Toilet paper

The use of which is obvious.

Doll that wets

Available in many places, though many are rather poorly made and leak like a sieve. Still, if you can get water into the doll through the mouth and then back out from the nether regions, it will suffice.

Underwear to fit the child

Regular "big kid" underwear, not pullups. It should fit a little loosely, definitely not too tightly. You'll probably need several pairs.

Cleaning rags

Your child will have accidents. This training method uses those accidents to correct the behavior. It also teaches the child how to handle those accidents on his own.

Liquids (juice, water, lemonade)

The more your child drinks, the more frequently he'll need to urinate, and that's vital to this training.

Salty snacks (pretzels, chips, nuts)

The snacks are used as rewards and motivation in part of the training. Salty snacks make the child thirsty, so he drinks more, so he needs to urinate more, so you have more training opportunities.

"Friends-Who-Care" list

List of about 10 important people to your child. Mom and Dad, older siblings, other relatives, neighbors, or teachers. They should be toilet trained themselves already, so don't pick peers. They should be people the child knows and loves, not someone who intimidates him. One or two fictional characters might also make the list - Cinderella and Belle were on ours.

Step 2: Is the Child Ready?

To start potty training, the child must have certain skills:

Able to walk. You just have to wait for this one.
Bladder control. Diapers should stay dry for several hours at a time, followed by a large urination, rather than the nearly constant dribbling of small infants. Something else you just have to wait for.
Manual coordination to pull his own underwear up and down. Down is usually pretty easy, up is sometimes a little tricky. Encourage the child to help pull his own pants up and down when you dress him during the week before you toilet train.
Ability and willingness to follow directions. Give him a simple test: ask him to do half a dozen things, like "Point to your nose, ears, hair," "bring me that toy", and "sit down on this chair" If your child is rebellious and refuses to do what you say just because you said it, you have some training to do (of you and him!) before you can start potty training.

Step 3: The Big Day: Setup

You'll spend The Big Day, from after breakfast to late afternoon, alone with the child. Kick everyone else out of the house - perhaps your spouse can take the other kids to the park and the museum, or over to Grandma's. Cats can probably stay around, but dogs with their infernal noses stuck into everything ought to go in the backyard or over to a neighbor's house.

The potty chair should be placed somewhere convenient. We used the bathroom (surprise, surprise). The Book says you can use a different room, like the kitchen, but I think that's stupid - your child needs to learn that the bathroom is where all this action happens, and putting the potty chair in a different room means he'll be carrying the full pot through the house for disposal - it's like you're setting him up to fail.

Get your snacks and drinks ready. We left a basket of snacks on a shelf in the bathroom; you can use your pockets instead. Kids have a fairly short attention span, so you don't want to have to trek to the kitchen and back each time he needs another reward.

Step 4: Training the Doll

You'll start by illustrating what to do with the doll.

The doll should be dressed in underwear or training pants, just like the child is.

Have the child give the doll a drink. Most of these dolls come with a bottle designed to fit their mouth. You may have to squeeze the bottle or the doll to get the water in.

Tell your child that the doll needs to urinate (or pee, or go "wee-wee", or whatever term you choose). Take the doll to the potty. Have your child help pull down the dolls pants and sit her on the potty chair. Now everyone must sit quietly for a moment.

Tell the child to look between the doll's legs, and cause the doll to urinate, by squeezing or pulling the plug or whatever.

Praise the doll enthusiastically. "Dolly is a big girl, she peed in the potty!" Encourage the child to also be enthusiastic, clapping his hands. Offer the doll a snack - one pretzel, or one chip. Of course, the doll can't eat it, so ask your child if he'll be a "big boy" and go in the potty. If he says he will, then he can have the snack instead.

If your child is female, she'll have to wipe even after urinating. Assist the child in tearing off one square of toilet paper and wiping the doll.

Guide the child through emptying the potty chair into the toilet and flushing the toilet. He'll have to:

Lift the lid
Pick up the pot with both hands
Empty the pot into the toilet without spilling
Hold the pot in one hand and flush with the other
Replace the pot properly
Wash their hands
Exit the bathroom

Step 5: Dry Pants Check

This training method emphasizes having dry pants more than going to the toilet. Have the child check if the doll's pants are dry. They are, so offer the doll a snack. The doll still can't eat it, so have the child check if his own pants are dry (he should actually feel his pants with his hand). His pants are dry, so he gets the doll's snack.

After a couple of minutes, repeat two or three times. Switch around the treats offered to keep things new and exciting. Use the juice, lemonade, or water too.

Step 6: Doll's Accident

Time to handle an accident!

Distract the child, and make the doll wet herself, or pour some water over her pants.

At the next dry pants check, the child will discover the wet pants. "Oh, no, dolly!" you'll say. "Big girls don't wet their pants!"

Now, the doll has had an accident, so the doll has to practice going potty. Help the child take the doll very rapidly through the whole process: go to the bathroom, pull pants down, sit on the potty, stand up, pull pants up, empty the potty, wash hands, leave the bathroom. You won't actually have the doll wet, or flush the toilet, or wash hands; it's enough to just sit down and stand up and put your hand on the flush lever and tap the sink. This whole process should take about 20 seconds.

Change the doll's pants. Do another 3 Dry Pants Checks, and another successful trip to the potty

That's about it for the doll's role. Now it's the child's turn.

Step 7: Trial Runs

Every 15 minutes, have the child go on a dry run. Walk to the potty, pull pants down, and sit quietly for several minutes. After a time, he can stand up and pull his pants up.

How long must he sit there? 10 minutes at first. The objective here is to coincidentally be sitting there when the urge to urinate arises. Once he's urinated in the chair, the sit time during a dry run is 5 minutes.

Step 8: Success!

At some point, the child ought to urinate in the potty during a dry run. You must be watching carefully, and the moment the stream begins, praise him enthusiastically. "You did it! You peed in the potty! You're such a big boy!" This is not the time to be proper and formal. "I say, old chap, bravo, wot?" goes nowhere with a child. You should be clapping your hands and jumping up and down in excitement. Be sure to tell him why you're so happy - this isn't the time for unconditional love; this praise is driven directly by his actions.

Now, he has to go through the process of emptying the potty himself. Stand by to prevent spilling, but emptying the pot is his job, not yours. At the beginning, offer praise for each step. "You pulled up your pants! Hooray! You picked up the pot with both hands! Good job!" As the day progresses, you'll offer praise only after completing larger sets of activities. "You went potty! Yippee!"

The "Friends-Who-Care" list comes into play here. Go down the list and mention how pleased each person will be with the activity. "You're sitting on the potty! Daddy will be so proud! You emptied the potty! Grandma will say you're a big boy! Your pants are dry, just like Cinderella keeps her pants dry!"

Step 9: Failure (not)

Eventually, the child will probably have an accident. Not failure! Vital to the training!

What not do to: punish them. No yelling, no scolding, no spanking, or anything else that conveys anger. Yes, you're displeased, but we'll handle it differently.

What to do: In a loud (not angry, just loud) voice say, "No!" Then calmly explain the problem. "You wet your pants. Big boys don't wet their pants! Mommy never wets her pants." Now, since his pants are wet, he has to practice going potty. Practice quickly! Run to the potty, pull pants down, sit for a second, stand up, pants up, and back to the scene of the accident. 10-20 seconds here.

Here comes the hardest part of the day: Practice 10 times, starting from different locations in the house. That means going room to room, with a child in wet pants, and back and forth to the bathroom.

Truth in advertising: my kids were in tears by the 4th run. Pulling wet pants back up is no fun at all, and being hurried in and out of the bathroom while soggy is frustrating. We'd often quit by the 7th run.

After the quick runs, do 10 dry pants checks. Of course, their pants are wet, so the checks fail. Express disappointment, and how people on the "Friends-Who-Care" list will be sad. "Are your pants dry? No? Oh, no, Daddy never wets his pants. Are your pants dry? No? Oh, cousin Billy doesn't pee in his pants, he pees in the potty!"

Now the child may change into dry pants. Show him where to put the wet pants, have him put on the dry pants himself, and if necessary show him where to get a rag and dry any puddles he left on the floor. This step really shows the uniqueness of this method: the child is responsible for everything, including cleaning up his own mess.

Step 10: Putting It Into Practice

The child has now had all the training that is necessary, and needs to practice. That means dry runs every 15 minutes, dry pants checks every few minutes, plenty of praise for successfully peeing in the potty, repeats of the quick runs for accidents. You'll still be giving him as much liquid as he can handle to give plenty of opportunity for correction.

At some point, the child ought to head off to the bathroom on their own. Follow along, but remain quiet until he has completed the process, then explode in delight - this is a major milestone, and you better make sure your child knows it. We let our kids call Grandma at this point and tell her what they'd done, so she could get excited too.

If all went according to plan, you're pretty much done with toilet training, other than doing dry pants checks (every half hour, tapering off to about 6 times a day) for the next couple days (you won't give treats for them anymore, just verbal praise).

Step 11: Troubleshooting

Although the book's title says "Less than a day", and the authors layout an ideal scenario that finishes in a few hours, it took us a little longer.

With my oldest daughter, my wife started training using no particular method earlier in the week. It was not much fun for either of them, none of the lessons seemed to be sinking in, and they lost patience with each other. I picked up the reins over the weekend using this book, and things went much smoother. We had two or three accidents to clean up, but that's part of the training. In the following weeks, she only had a couple of accidents, and those were when she was someplace where a toilet wasn't handy - out in a store, in the car, and when she locked herself in the bedroom and my wife had to kick the door in.
My youngest daughter had unbelievable bladder control. On the day I tried to train her, she went all morning without any action, and finally I had to put her down for a nap. She woke up soaking. This continued for several days. We finally decided to put her in pullups anytime she was in bed, and regular underwear during the rest of the day. This went on for several months, until we saw that her pullups were consistently dry when she woke up. The book allows for this - children under 2 1/2 years can be expected to keep pants dry during the day, and sleep in pullups or diapers.
The book emphasizes that you should not punish your child during this training, since it creates an aversion to the whole toileting procedure. We carefully avoided any punishment at the time of an accident. However, during some of the quick runs, our daughters became defiant and refused to follow directions, so we followed our usual course of action for disobedience. We also cut the number of practice runs short, because we were growing frustrated, and it's hard to learn anything in that state of mind.