DD toilet trained at 2 years 6 months in 3 days - never had an accident. Day dry but stayed in night nappies another year.
DS1 toilet trained at 2 years 9 months in about 5 days - bit more effort (key seemed to be not wearing underpants as they felt like a nappy - bare bum at home and loose baggy airy shorts out and about). he had a couple of accidents the first day and maybe one on day 3 and one on day 5 and then never had an accident again. He was also night dry from the first nappy free day and never has wet the bed, ever.
Both DD and DS1 asked to stop wearing nappies - DS1 asked to stop wearing them at night, which I didn't expect to be a success but it was, right from the first night.
I thought the key was to wait til they suggested it... cue DS2, whose entire reason for being has been to show me that I was getting complacent thinking I knew what I was doing and that everything, in every area of parenting, that worked with DC1 & 2 would not work with him :o
DS2 never asked to potty train and was still in nappies at 3, having tried and failed at about 2 years 9 months and again at about 2 years 11 months (no interest, just acted as if he had a nappy on and peed/ pooed, and didn't produce anything on the toilet). He said he liked nappies and wanted to stay a baby (a very bloody articulate baby!)
When I bribed him with something he really, really wanted (golden underpants... who knows why... and a light sabre) he tried really, really hard at about 3 years 3 months and cracked it. Quite a few accidents but he was focussed and actually wanted to (but for the reward, where the older two had wanted to get rid of nappies). In the end he cracked it in about ten days and after that had very occasional accidents - maybe once a week for a few weeks, then for a few more months he might have a very rare accident, maybe one a month. He was 100% reliable before he turned 4 at least...
The child has to be motivated in some way, whether intrinsically (which is the best way obviously) or by a reward.
If you see no progress at all after 3 days just put the nappy back on and try again in a couple of months.