Obviously for work experience, you’re not getting paid (in most cases), so you’re asking the company to help you out by giving you some experience.
It is difficult, because in many ways, they are doing you a favour, but you should try and make it sound like you’ll be an asset during your time there. You should include why you want to do it, what you can bring during your time there and also what it will all be aiming toward.
Some companies may also pride themselves in giving out work experience placements to people who then go on to get very good jobs, so make it sound like it’ll be worthwhile for everybody!
Basically, sell yourself. Talk about your good qualities, any other bits of experience you might have had, and your qualifications. At this stage, you’re unlikely to have a wealth of experience and large amounts of things to talk about, so major on the good things you’ve done so far.