Work experience is forced on all school pupils at one time or another, at least in Britain. The idea is that the pupil will find out what working in the real world is like. As such, she or he is thrust into a business, pretty much at random, for one or two weeks. They don't get paid, and are usually expected to perform all kinds of menial tasks.

In effect the experience is almost nothing like the experience of working in the real world, unless you have a great hankering to have a job making tea or coffee for the rest of your life.

Some students are lucky, and find themselves in a business that makes a good attempt to provide an authentic working environment for them, and doesn't treat them as lackeys. The Guardian is famous for this.

What you need in order to get a job. If you've already had a job, it's easy to fulfill this requirement and get a job. Otherwise, you'll need to get some work experience first.

Evidently this vicious cycle can be broken, since people (among them myself) do work. How this happens is unknown, even to the workers. But you can trust me: as someone who once had no work experience and now has a job, I can tell you that it is possible.

But I still don't know how, exactly.

This is something I am doing currently (as in right now).

Work experience doesn't just cover working in school affiliated programmes, it covers anything involving you and working. Start with anything you can get your hands on. I worked in Victoria Wine for 2 years of no thanks. What experience was relevant to working with computers? Working with people of course, which counts for a lot.
You can't expect to just get a job that requires a certain amount of experience, you need to work you way up the food chain first. Any experience is better than none, especially if it shows you are capable of getting off your arse. If you want a job in an area you've never worked in before, go for the graduate or new starter jobs. They are there, you just have to look.

The moral of the story?
The more experience you have, the higher up you are. After experience stops mattering you probably don't have to worry about moving up anymore.

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