J.,
I started training my daughter after she turned two, and sometimes she would tell me that she needed to go and sometimes she would go in her pull ups. I notice that when she has a cup of milk or juice, it's usually about 15-20mins later she would have to go, and I would put her on the toilet. I introduced the disney princess underwear to her, and she was real excited to wear them, so that helped. She had accidents every now and then.. we started her wearing her underwear for a few hours here and there, and eventually longer, till it was just diapers when we go out, and eventually only at night, and slowly I stopped letting her drink about 2-3 hours before bed, and started letting her wear her underwear to bed. I think the most important thing is her understanding of her body, and her bladder control. I know at the begining, she would go on the toilet, and say 10mins later her diaper would be wet again...
I talked to her and explained that the diaper was dirty and made her butt stinky, and when she would wet her diaper I would hold my nose and tease her that she had a stinky butt, and when she was good and wet on the toilet we would clap and kiss and praise that she did good. (It was funny cause for awhile whenever she went on the toilet she would make us clap if we forget to praise her)....
Now at 2 years and 8 months, she can hold her bladder through the night, and would wake up early morning around 5am (if she had to something to drink at night) to have me take her to the bathroom and then she would go back to sleep. Overall it took us about 3-6months to learn the whole process.
Good Luck with your little one and let me know if there's something I can help you with!