Most banks will require that you go into your bank branch to apply for online banking. Some banks will allow you to set up your online banking over the internet, but won't allow you to transfer money or pay bills until you visit a branch to verify your identity. You will need to take your ID book and details of your bank account with you when you apply. If you don't yet have an account at the bank, you can ask for internet banking when you are setting up your account.
Most banks include internet and telephone or cellphone banking in the same package. This means that if you sign up for internet banking you will also be able to get account balances and make payments over the phone, using a special password. That way, even if you don't have access to a computer, you can still pay your bills without having to go to the bank or ATM.