I don't know if it is because there isn't enough training going on, or if it is compounded by the fact that people don't want to do them.
A small rant to give some context to that, and then I'll answer what I can of your question.
The problem with the educational system today is that everyone is expected to get a college degree to do jobs that didn't used to (and, honestly, don't even really) require college degrees. That's a serious problem because it's turned a Bachelors into the new high school diploma. Colleges make money off of that assumption, and are under as much pressure to pass people with degrees as they are happy to take peoples' money. Now having a Bachelors means almost nothing and Masters degrees are starting to get that way too as the cycle continues.
What people don't realize is that while college degrees are fine and good (I have one, I don't regret it), they really aren't good for anything except academic careers, highly specialized careers like engineers and doctors, or science careers. And everybody thinks they're above skill trades for some reason because those don't require degrees. Those require actual labor and you take a nontraditional approach to learning them.
I know more plumbers that live in mansions than I do doctors.
They're practical, have good job security, and they're accessible to people who aren't willing to go through the extra bullshit to get a college degree (again, have one, but I had to do a lot of bullshit to get it: e.g. B.A. in Writing with a minor in Pyscholinguistics and Cognitive Psychology, but I almost didn't get it because of a second year German class... I WAS A FUCKING ENGLISH MAJOR).
To answer your question:
It depends on what route you go. There are courses in a given job you can take at trade schools or through correspondence courses, or you can shop around to local companies and ask if they take on apprentices or can give you any advice on where to get started to enter the field. The one thing I learned from when I was looking at being a locksmith was that the best people who can answer your questions are the ones doing it at the moment. They might even be willing to take you on as an apprentice someday. Some might offer you a job as a cashier or something while you take your classes, some might let you shadow them for a while to see how the job goes.
It takes a while and has lots of hands-on training on top of any other studying you have to do, but again, most trade skills have pretty high demand and good job security.
Construction is different. Contractors are better as far as I know. And both of them are very, very seasonal. Plumbing and electric work have a degree of being season-prone to them because they work with construction and contractors, but the seasonality is nothing like construction. You still need plumbers and electricians during winter, sometimes especially (pipes freeze, power goes out, etc). With construction you can do shit all during winter.