Just following on from KembleTwins' post - we also make sure we give our w-e students a desk, a computer ID, a person who they can ask for help at any time, and a small project to work on, ideally something real. When there's time, we like them to do a presentation of their work at the end, someone makes a little speech to thank them for their work, and they're given a present. We now seem to have a tradition where the students make fairy cakes for their last day, which we're all enjoying very much!
When students do w-e, we try to give them something interesting and skill-developing, whereas our students who are doing paid work do real work, which is often very dull!
If you're contacting companies directly, it helps a lot in finding useful projects if you have a clear idea of what the young person can and would like to do, together with some examples - e.g. if you can say 'Having studied Art GCSE, I am a keen graphic designer and can use a number of web packages. I have designed leaflets, posters and web sites.' or even something like 'I am good at research, and can quickly find out accurate information from the web and from libraries.'
It's probably also worth trying to guess what people will assume students can deal with without any training - in an software company, for example, people will probably assume that students can use a computer (both PC and Mac) and a number of common software packages without any training or instructions.