You can take payments online in a number of ways. The first is PayPal, an inexpensive way to start taking payments quickly. With PayPal, your visitors can pay with a credit card or by sending a payment from their checking account. PayPal provides a shopping cart and many other free services that are helpful to sites that are starting out. They charge 2.9% plus $.30 per transaction and have no start-up fees. PayPal, however, is not a very customizable solution, and it can have a "start-up" feel. However, this is changing and many mainstream sites are now accepting PayPal as more and more people have PayPal accounts. PayPal provides a very easy way to integrate a shopping cart into your site, which reduces development time.
There is also the option of creating a full e-commerce solution. This involves many different components - a merchant account from a bank, a payment gateway service that allows you to accept payments into your merchant account from your website, a shopping cart or payment script that integrates with your payment gateway, and certain elements of the server environment like having an SSL certificate and a static IP. Full e-commerce is much more expensive and time-consuming to develop than PayPal, but it can be integrated into your site for a truly seamless payment experience. It can also save you money in the long run if you are doing a lot of sales.