The timing of potty training is largely a matter of preference. Which do you like less - changing diapers or cleaning up puddles and messy undies?
Early potty training takes longer than late potty training, but it can save you over a year of changing diapers. It's easier to deal with the will of a 20-month old baby because they're used to being told what to do and so potty training is just another thing to learn. The hardest part is getting a mostly non-verbal child to understand what it is you want of them. How do you explain 'going potty?' So it takes a while for them to understand what they're supposed to do.
Late potty training (age three or after) is done with the full understanding of the child, but that means that you have to change diapers for awhile longer. It usually goes a lot faster, which is nice.
What is the most difficult is potty training a two year-old. They understand what you want but often don't want to do it, and the will of a two year-old is amazingly strong. I've run into enough two year-olds to realized that in a battle of wills with them, you will lose every single time. So I very carefully chose what to clash with two year-olds with. If I can't physically force them to do something, I usually don't make an issue of it. Which includes potty training - it's impossible to make a child pee in a toilet.
In order to train a toddler to be potty trained with my method, there are a few prerequisites. The child has to be obedient. My method involves a lot of sitting around on their toilet, and if they won't sit for long periods of time, you're going to have to find another method. You also have to have a little potty - no toilet seats allowed, unless you want to spend your entire life in the bathroom.
Also, you have to understand what I mean when I say 'potty trained.' I mean a child that goes on the toilet when you put them there and doesn't pee anywhere else. They wear underwear during day, during naps, and at night. What they don't do is use the toilet on their own. Toddlers that young aren't capable of doing that - yet. At first you will have to take them to the toilet at set times - usually when they wake up, at mid-morning, before nap, after nap, and before bed. After several months, they will start telling you that they need to use the bathroom. And within a year, they'll go on their own. It sounds like a long time to being fully potty trained, but that year was an entire year of you not changing diapers. If you can change diapers, you can take your child to the bathroom.
I realized after potty training a few children that toddlers have no problem not peeing. They can, under the right circumstances, hold their bladders for quite a long time. The difficulty with potty training, then, is not teaching them to hold it, but to release it in the proper place. That is the skill they have to learn - to let out urine in a controlled manner.
So with this in mind, I start the first day with sitting the toddler down on the toilet and leaving them there until they pee. It usually takes an hour or two and they will be very unhappy about it. They're not used to being without a diaper, and when they've been without a diaper before (bath, changing their diaper), they're used to not peeing. So their bladder will get uncomfortably full and they'll fuss and cry before they finally can't hold it anymore and they pee.
So do whatever you can to keep them on the toilet. William sucks his thumb, so he has his blanket. I strew toys around him. Give them electronics, let them watch a movie, just don't let them off the toilet until they've gone. After they go, show them the toilet with pee in it, make a big show of how happy you are, cheer, high-five, tell them multiple times that they've peed in the potty, and then give them a treat. William loves jellybeans, so I've been using them. The whole point of this is to have them associate peeing in the toilet with good things and help them to understand what peeing in the potty is.
Give them a two-hour break and then put them back on the potty until they've peed again. This will take another ridiculously long amount of time. I call this stage the Iron Bladder stage. They don't yet understand that it's okay to pee outside their diapers, and so using the bathroom only happens when they just can't hold it any longer. During this stage it is essential to leave them on the potty until they've peed. Don't let them off until they've peed because, inevitably, they will pee as soon as you let them off. The longer they're sitting, they closer they are to peeing, so if you give up after 1 1/2 hours, it's not going to end well.
The next stage is Mouse Bladder stage. You'll know when you're in mouse bladder stage because your child will sit down, use the bathroom within half an hour, get up, and then have an accident twenty minutes later. Sometimes they'll let out just a little pee, get off the toilet, and then let out some more pee. They are starting to realize that it's okay to pee outside the diaper, but they don't know how to let it all out at once. So they let out a little and then stop. You are tricked into thinking that their bladder is empty, you let them go play, and then they let the rest out.
This stage is maddening. You feel like your child will never potty train, the puddles of urine will never end, and that there is regression, not progress. This stage is when you'll want to give up because it is clearly not working. But press on, because mouse bladder stage shows that your child is starting to understand.
When they do have accidents, explain to them firmly (try not to yell because then they get confused about whether or not they should pee. It's hard, though, so don't beat yourself up if you do. I've done a lot of yelling in my time) that it's bad to pee on the floor, give them a little spank, put them on the potty, and give them a kiss. Chances are good that they've still got some urine left in their bladder and they can finish on the potty. Once again, don't let them off until they've peed. Leaving them on the toilet for long periods of time gives them the best opportunity to be successful - and being successful is what potty trains a child.
The last stage is Controlled Bladder stage. You'll know you've reached this stage when your toddler goes on the toilet within five to ten minutes of you putting them down. I still put them in diapers when I go out (but I try not to go out much at all during the first two weeks), and if they've reached controlled bladder stage, they will have dry diapers when you come home - they can usually last about three hours. At this point, if you put them on the toilet and they don't go within twenty or thirty minutes, you can let them up again for another hour or so because they can hold it.
After a week of controlled bladder stage, you can go to all undies all the time (when you're at home. I put them in diapers when I go out until they're capable of telling me they need to use the bathroom). There will probably be some nights where they wet the bed, so make sure you have a waterproof mattress on the bed, but they will eventually figure it out.
One thing I don't like about night- and nap-time undies is that I can't let them languish for hours in their bed while I sleep in or ignore them in the afternoon after their naps. It's somewhat obnoxious, but I learned the hard way with Joseph that waiting is a bad idea. There is a window for night time training where they're naturally ready for it and if you wait too long (more than a month), it will close and then night time training will be very painful. So don't delay.
I usually transition to a regular toilet when they are around two and a half. When we go on R&R in the summer, I have no desire to pack a toilet in my luggage, so usually I tell my toddler that the red potty (ours is a red Baby Bjorn one) has disappeared and they have to use the big one. They still ask for assistance and I hold them on the toilet so they're not scared, but eventually they just decide that it's easier to go on their own rather than come and get me. It's always a happy time when that happens.
So, there are all my secrets for early potty training. I still hate potty training, but I'm happy to know that I've definitely reached the majority skills level for potty trained children. There is no way I'm going to have six more children, so I can be happy in knowing that there are a very, very few number of children left to potty train. Hallelujah!