Paypal has long been the "simple" answer
A popular alternative to a full merchant account, particularly for beginning developers, is to use PayPal. PayPal can be used in a couple of ways, but the older, traditional PayPal model has PayPal processing payments internally: from the customer’s PayPal account to yours. If you want to get the money into your bank account from PayPal, you can do that after the fact. Again, PayPal has services that can be used in other ways, including taking credit cards, but this is the standard PayPal model. The PayPal fees tend to be lower than the payment gateway-merchant account route, but your money ends up in PayPal at the end of the process, not in your bank account (until you transfer it).
How Paypal Works - But...the user experience of Paypal does not reflect this simplicity
A Conventional Payment Gateway-Merchant Account System
In an e-commerce site, you take a customer’s billing information and pass it, along with the order information (e.g., the total), to a payment gateway such as Authorize.net. This an intermediary between the credit card companies and a merchant account. The payment gateway confirms that the charge can be made to the customer’s credit card and passes that charge information to the merchant account. The payment gateway will report the results back to your site, too (of course). The merchant account is what actually allows your business to accept credit card transactions. It coordinates the credit card transactions with your bank account (i.e., getting you your money).
This is the basic premise. Note that you can’t just mix and match pieces here willy-nilly. Different payment gateways and merchant accounts will accept different card types. And different payment gateways, merchant accounts, and bank accounts are setup to work together (or not). Your bank may also be able to act as the merchant account. Oh, you should also know that there are many fees involved here. The payment gateway will charge a fee and the merchant account will, too.
Lets look at how payments move via a Conventional Gateway - Merchant Account.
And now for something completely different... a system called "STRIPE"
So how is Stripe different? First, Stripe is a “full-stack” solution, meaning Stripe acts as both the payment gateway and the merchant account. Your Web site communicates the customer and order information to Stripe, Stripe clears it with the associated credit card company, and Stripe puts the money in your bank account. And…that’s it. You don’t have to do anything special with your bank account to make this happen. It just works.
Why do I love Stripe? Stripe is crazy easy to use.