There are several ways to accept payments through your website. The easiest and most basic is to integrate a PayPal account or similar service.
This will handle all payment processing on your behalf. Users are taken to PayPal page where they register or enter login details and complete the payment.
A more sophisticated method is to set up a payment gateway with an Internet Payment Partner, such as SagePay, WorldPay or Secure Trading. You generally pay a monthly fee and zero or a lower percentage per transaction.
If you already have a facility to accept payments in your ‘brick and mortar’ shop you can probably easily upgrade your service to include online payments.