Hi B., the amount of time it takes really all depends. Often if you wait longer, it takes less time. My daughter trained in 4 days at 3 yrs, 1 month. I started with my son at 2 yrs 11 months and it took about 2 months (to get to the point where he wasn't only using the toilet all the time but telling me had to, it only took a few weeks for him to use the toilet consistently). I purposely waited til my kids were older because I had no interest in months and months of "training" and accidents, etc. For me, it was just a personal preference to have a child in diapers than one who was kinda, sorta, but not really a little bit toilet trained.
At a little past two, many toddlers see the potty as a game, they think it's fun but they don't really recognize the urge to go yet. The use of disposable diapers and pullups don't give kids much motivation to use the toilet, even with those "feel wet" liners, when they pee, they're not really feeling wet. And if you start with pullups and she's using them as a diaper, she isn't going to suddenly stop using them as a diaper and see them as "underwear." A change to cloth can help kiddo's to understand what's happening in their body - that when you pee, you get wet, and then to recognize what it feels like just before that happens.
If she's recognizing the urge to go but still asking for a diaper, I'd suggest telling her that it's okay to pee or poop in her diaper, while she is sitting on the toilet or potty. This gives her the comfort zone of her diaper while learning that the toilet is where we "go."
With my son, I used thick cloth training pants with vinyl waterproof liner and took him to the toilet about every hour and a half, no asking if he had to go, just took him. The first 2 weeks, he'd never actually make a deposit on the toilet and would wet/soil every pair of training pants each day, but after that, he figured out that he should wait to pee or poop til I brought him to the bathroom and pretty much never had accidents after that.
Good luck!