I'm running a HP Elitebook 8570W for graphic design, but my school uses iMacs. I want to be able to connect my HP to an Apple Led Cinema display, but i don't know if this is possible?
As the Apple Cinema LED Display has a Mini DisplayPort input, you need a DisplayPort or Mini DisplayPort out on your computer, or you can look for DVI to Mini DisplayPort adapters (Mini DisplayPort to DVI adapters will not work).
Since this HP site says, that your HP has a DisplayPort output, you can get a DisplayPort to Mini DisplayPort adapter, probably via Newegg or MonoPrice.