I recently trained my 2 yr 10 month old using the 3-day method. I had tried twice before when she was 2 yr 5 months and 2 yr 8 months and failed horribly. Just ended up with wet pants and no real success on the potty.
The 3-day method sort of locks you in the house for 3-days and you don't use diapers or pull-ups at all. You are CONSTANTLY watching your child for signs that they are about to pee and rushing them off to the potty when you see it's about to happen. The idea is that the penny will drop and they will suddenly get that the sensation of pee means that they have to go sit on the potty. You don't make them sit on schedule or for 20 minutes at a time. You just constantly remind them to "tell mummy when you have to go potty OK?" I guess this way of phrasing it, puts the power in their court. Because even now, if you ask my DD "Do you have to go potty?" She'll say no and then 1 min later run to the toilet. I don't think they honestly know they have to go until the second before they need to.
It worked for us. It happened to be a really warm week when I did it, so I just let DD run around in a t-shirt and underpants. The first day we had NO success. She didn't once make it to the potty in time and went through nearly all of her new underpants (Like 10 pairs). It was halfway through day 2 before we had a victory. by lunch on day 3, she got it. I think she actually got number 2's first and then number 1's. It really was like the penny just dropped and she understood what the sensation was and that she had to run to the potty. We have had very few accidents since. I don't put her in a diaper during nap, so we do have accidents about once/twice a week. Kind of a pain, but I don't want to confuse her by putting her back in diapers during the day. We do use diapers at night still, but she is almost always dry, so thinking of getting rid of that crutch soon.
If you have the time and inclination to stay home for 3 days, they say this can work for kids as young as 20 months.
Good Luck.