Internships are a really constructive way to help you find out if you'll like a certain job or career (at least, this is what I'm hoping!) But - it's also important to remember that they are not the be all and end all - there are plenty of other ways to get experience and useful skills, especially at uni!
At the University of Oxford we have a great Careers Service - they run loads of workshops and talks about things like writing a CV, writing a Cover Letter, and funding yourself when you're doing an internship. They also have a great website with loads of resources. And, on top of all this, we have 'Careers Connect', which is an online careers platform advertising internships - these include summer internships and micro-internships, which are short one to two week internships taking place in any of the vacations.
You can also go your own way and contact various organisations you're interested in directly. This is one of those times when you have nothing to lose from just asking - the worst that can happen is that the internship person won't answer you or that they'll say no, and then you'll just be in exactly the same position you start in - so you've lost nothing. You can also do this whilst you're still in school - maybe you're looking for something to do over the long summer before you start uni? I've found it's best to contact small organisations. When you email them, you should find out the name of the person you're emailing - that way it's more personal and shows that you've researched them. You should also include a few short lines about why you'd be well-suited to the company - again, this shows research and interest! The main thing to do is sell yourself - emphasise why you'd be beneficial to them - an internship is a two way thing: they benefit from having you there, and you benefit from the experience, too.
Hope this was helpful!