Do the journey with them a couple of times. Talk them through it throughout the journey, i.e. let passengers off before getting on, waiting in a queue at the door, having cash or ticket ready to pay, where to put the ticket (i.e. zipped pocket etc), then awareness of when to get off, when to press the stop button on the bus etc. Obviously all of this is easier if you've been a regular bus/train user as they'll have watched you do it!
DON'T point out potential problems (such as what happens if the bus doesn't turn up or what happens if they lose their cash/ticket) in these first couple of journeys. Just concentrate on getting them on the right bus/train (i.e. look for the destination board on the front, look at train station departure board to look for the platform number, etc). Likewise DON'T make them anxious about where to sit, avoiding "dodgy" looking people, etc. There's a time and a place to highlight problem-solving, and the first couple of journeys isn't the time nor place or you'll just make them more anxious. It's hard enough for them to get used to the basics without stressing them out about all the potential problems.
Will there be other children on the same buses/trains going to/from the same school/activities? If so, they'll quickly make friends with people doing the same journey, or even if not "friends", they'll be more comfortable knowing others they recognise are going where they're going!
We just did a couple of practice runs with our 11 year old DS when he started secondary, on the bus from our village to the city centre bus station, and then did "the walk" between the bus station, through the city centre, to his school, and back. All of it was unfamiliar, he'd never done that bus journey before. We'd done a few park n ride buses and tour buses in other towns/cities, so he had a very basic experienced of buses. He knew no one going from our village to the same school. But, when the day came, he was absolutely fine. Got himself there fine, got himself back fine. Buses were busy which helped (so reduced risk of assault/abuse/theft etc). Biggest problem was the unreliable bus service, with services often late or cancelled, or a few times the driver not knowing the route and missing out our village stops completely, but he quickly sorted himself out, i.e. waited for the next bus, or if they missed out our village, he'd cross the road and catch one in the other direction to come back.
The more fuss you make, as a parent, the more anxious and stressed they get.