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For the payment, you get always a while on the pay agents' site. But at the end you will be returned to your site.
For other payment agents, you need to write a plugin. Use the PayPal one as guidance and follow the documentation of the payment agent. Several agents provide also some PHP sources for easy integration.
In general, the plugin is called at the payment step and provides some variables with references and the amount to be payed, togheter with some other parameters. After the payment on the agent site (entering id and eg card data) is completed, a mail is sent to the customer and vendor or some callback function may be called, confirming the payment.
