When the PayPal transaction is complete, PayPal shows this:
Thanks for your order
Your payment of $XXXX.XX USD is complete.
You\'re now going back to MYSITE.
You will also need a Website Payments Pro subscription for that. https://www.paypal.com/webapps/mpp/website-payments-pro
Once you have it, get the API signature, API username & API password from the My Profile area of your paypal account.
Then, use the Direct Payment method as described in the following manual https://cms.paypal.com/cms_content/US/en_US/files/developer/PP_WPP_IntegrationGuide.pdf
As mentioned by Watermark, you might need to review PCI requirements and at least have SSL on your site before you can do this.