mathanxiety, for some it may take more than a day to pick up those skills.
I'm visually impaired, hence no driving licence, and I did actually have training with a lovely lady, walking certain routes and learning bus routes etc. This was over a course of about 6 weeks, although obviously my case is different. I don't need a cane/guide dog but I do benefit from learning landmarks etc. Some people may have no vision problems or other sn, and it still might take them a while, everyone's different. I do think some kind of training would be good, maybe as part of PSHE or something, that's when mine was done.
Anyway, what I'm saying, in my usual rambly way, is that for me, it was very liberating but lovely to have someone there when I was first learning.
With trains, I went to places with friends first, then braved it on my own. I've only gone wrong once 
Tomorrow is my biggest challenge though, I'm going somewhere for 5 nights which will require me to change trains, which I've never done alone before, so that'll be an adventure.
I do use public transport wherever possible, but sometimes it's easier for me and safer to try and get a lift. Luckily my friends and parents (still live at home) are very good and will always offer - I sometimes turn the lift down in favour of a bus! But for example, at night, I prefer being picked up or getting a taxi because in the dark, it's harder for me to get my bearings. I always give petrol money, or in the case of one friend who won't take it, I give a bottle of wine every few weeks, which he will accept I think I kept him and his DP stocked on wine through the ice hockey season