You need to take some proof of ID, such as bank statement, drivers license etc, to set up your details with them.
They'll give you a CEX card or keyring fob card, to help with future deals, so you don't need to go through the above process with them.
Sometimes they'll ask for proof of purchase on some items, particularly phones.
They will test the phones, to make sure they work fine, and if they are unlocked etc, not reported lost/stolen.
They will grade the phones from grade A to C, A being the best, you'll get more money for grade A, than you will for grade B or C.
They either give you cash, or in store credit which is higher than the cash.
I've dealt with them a lot, and they've always been great, the only downside is their prices are slightly lower than you'd get on ebay.
Edit: Here's what the require, from their website
http://uk.webuy.com/help/storehelp.p...p_requirements