To open a PayPal account, go to https://www.paypal.com/ and click on the Sign Up link. You will be asked to choose from three kinds of accounts – Personal, Premier, and Business. If you just need the account to receive money and shop online, then personal will be fine. If you are an online seller, you will be better off using premier. The first kind of account is free.
While you do not need a credit card to open a PayPal account, you do need a bank account. When inputting the details, make sure that your name and address match the details in the bank account that you associate your PayPal account with.