A very good question!
Astronauts go through very extensive training before they get to go to space (up to two years worth of training before they can go to launch), and even people who go up as “space tourists” still have to undergo pretty significant training. Sarah Brightman, for instance, plans to be on the ISS for 10 days; her training will be 9 months long, in addition to costing her several tens of millions of dollars.
As our space program advances, I would imagine that the training needed to go into space will decrease dramatically. If we use airplanes as a parallel, in the early days of airplanes, just to get on the plane you had to be highly trained in all aspects of operating, landing, and surviving failures. Effectively, if you weren’t performing a critical role in making the plane work (in other words, a pilot), you weren’t on that plane. But nowadays when you get on a plane, after a lot of development of the technology that goes into reliable planes, the majority of people on board are ‘trained’ in the sense that they will mostly try to ignore the instructions on how to put on the oxygen mask in case of cabin pressure loss. The pilots are functionally invisible to most of the passengers.
I expect that once space travel has advanced to the point where we can transport large groups of people, there will be less of a requirement that every person on the spacecraft will need extensive training. Obviously we would still need highly trained people to operate the spacecraft, but for the majority of people on board, they’d just need to know what to do in case of an emergency, much as we do now on planes.
The reason everyone needs so much training to go into space right now is because every single person on the craft has a vital role to play to make sure everyone gets up and down safely, and can complete the mission that needs to be done while in space. This is one of the reasons that the only astronauts on the space shuttle who weren’t extremely talented Air Force pilots were the mission scientists and payload specialists, and while they weren’t expected to be able to land the Shuttle, they were entirely responsible for making sure that the science happening in space was taken care of, and they’re usually the ones that wind up on spacewalks. Spacewalks (among other things) serve the critical purpose of repairing or maintaining equipment - either satellites, the spacecraft itself, or the International Space Station. This kind of repair is very technically challenging, so it requires the intensive years of training that the astronauts have to undergo.
However, if we’re transporting large groups of people, we will be able to move more people than just the mandatory operating crew, much as planes now do. While the operating crew will be able to take care of the flying of the ship and any repairs that need to be made, and the remainder of the people on board just need to avoid doing anything hazardous or dangerous to themselves or their ship. This will probably require a safety briefing (please do not poke holes on the ship, do not bring explosives on board, no smoking), but it wouldn’t require nearly the years of training it would require to be a pilot on that same spacecraft.