I presume you've already found this help page subsection that explains how to set up our Aweber integration:
http://www.e-junkie.com/ej/help.integration.htm#aweber
To do this for a specific product, you would checkmark "Sent transaction data to a URL" in that product's settings and click Next, then paste your Aweber integration URL (explained at the link above) into the product's Payment Variable Information URL field, then click Next until you can Submit changes.
When you have a product set up in your E-junkie Seller Admin, we provide ready-made HTML codes for your Cart or Buy Now button, which you would simply copy from us and paste into your page, wherever you want the button to appear. These help pages explain more about the differences between Cart vs. Buy Now buttons and how to obtain and use them for your site:
http://www.e-junkie.com/ej/help.buttons.cart.htm
The buyer would click your E-junkie Cart or Buy Now button to order the product and proceed to PayPal for checkout. When PayPal confirms to our system that they have completed the buyer's payment, we would then process the order for you, including sending the buyer's name/email to Aweber for subscription to your list there. Aweber would then send the buyer an opt-in confirmation email with a link the buyer must click to confirm their wish to subscribe.