I've found it's different with different children. My first, a very verbal child, started potty training herself at 18 mo. I was pregnant and did very little except have a few potties around the house and let her be naked a lot. She just started using it one day and that was it. She probably only peed on the floor a few times. She wasn't night trained until about 3 (I did use pull-ups at night) when she told me no more pullups. She probably has had 3 accidents ever. I did nothing,I wish I knew how to make my next child repeat that LOL. I *know* I just really lucked out with her.
So my son I started the same deal, about 24 months he started being interested in what I was doing (handing me toilet paper, etc) so I got the potties out. I could get him to sit before bath (we'd read a book) and we did that for awhile, he would not use it at all in the daytime, and would pee on the floor like no big deal. So I casually started at 24 months, never pushing (he would tell me NO and I'd just accept it) but closer to 3 he finally really got it, and potty trained at 3. And he still had accidents at night until he was 5. Even at age 3, IRL, he was one of the youngest boys I knew. Most pottylearned/trained a little older than that, closer to 3.5 I'd say. Girls were younger, prob more like 2.5.
My youngest is 20 months and has been showing interest. I've been letting her have lots of naked time, she rarely has an accident on the floor (she'll hold it or bring me a diaper) and I've had the potty out for a month or so. Today she drug the potty to me and she had peed in it! So I clapped, said "pee pee" and pointed and she clapped too. So I cleaned it out, and she sat and did it again! She ended up peeing on the little potty a few more times before bedtime...so we'll see how she does with me keeping her naked and the potty out. I'll add she's decently verbal. Not as much as DD#1 was, but more than my DS was.
My point being...some kids just really "get it" young, some don't but I've found (from also working at a daycare in the 2-3 yr old room) that you can't PUSH them when they don't want to/aren't ready. Potty learning/training is totally up to them. You can give clues (have potty out, talk about it when you use it, or changing their diaper) but it's really up to them to really take the lead. I have found that the harder you push, often, the more they push back.