Unlike other ecommerce necessities, this is normally not included with your ecommerce web hosting. There are currently 2 main options. Get a merchant account and charge your customers credit cards yourself, or leave it to a 3rd party payment processor company. This is most often done without any involvement from the web host, but they may help you by recommending merchant accounts/payment processors.
If you are planning on getting a merchant account and to the CC processing yourself, you need access to a secure server. A dedicated server is also an advantage, especially if you want to store your customers CC numbers. Dedicated servers are just far more secure than a shared server, and you don't want to be responsible for what happens if someone hacks into your server and steals the CC numbers you have stored.
3rd party payment processing is easier, and you have less to worry about. It is easy to set up, and the CC processing company does all the hard work. On the downside, it is more expensive, and it looks less professional if some other company's name shows up on your customers CC bills. Make sure you tell your customers what is going to show up on their CC bills to avoid any chargebacks and confused customers. Popular third party payment processing companies include PayPal, WorldPay and Protx.
