We never 'trained' DD as such - when she was 2.11 she started asking if she could go to the toilet - we were on holiday at the time and only had nappies, not pull ups or pants, so it was a bit awkward when we were out and about, but we started to get her to sit on the loo in the morning and before bed.
By the time we were back off holiday she was pooing on the toilet all the time but still wetting her nappies.
When we got home we tried pants for a day or so, but after three accidents decided not to bother just yet, but we did replace nappies with pull ups.
We would ask her if she needed a wee when we went and she would occasionally ask to go herself but we didn't do any rewards / encouragement etc (other than praise when she did do a wee on the toilet). If she wet in her pull up we would just change it.
She asked a couple of times if she could have pants on and we told her she had to go three days without a wet pull up and she could.
Within a month of coming back off holiday she was dry and in pants and has only ever had a handful of accidents - either when she has been asleep or just a bit distracted. She also never really used the potty - just went straight to the toilet.
She's still wet at night though - but we are using a similar method. If she's still wet at night when she is 7, then I'll worry!
This 'in her own time' method seems to work best with DD for most things though. If we try to 'train' her to do anything, she just rebels, we just tend to explain things to her telling her the benefits and how grown up it is etc and let her make her own mind up about when she wants to do it - sometime with a little bit of bribery thrown in for good measure!