When you buy a pay-as-you-go phone you get a little card about the size of a credit card. This card has your phone number on it, so when you top up you just give the shop your card and they stripe it to show you have paid so much money (say �10)
Your phone is then topped up with that amount, and you pay for it with cash, debit card or whatever.
The problem with pay as you go is that you pay much more "per call" than you do if you have a monthly contract.
Also if you have no credit you cannot make any calls.
If you go for a "cheap" contract (mine is �11 a month) they give you a free phone, and calls are much cheaper. Plus you never run out of credit.