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.