You can do it many ways. One way you can i guess it would be best solution, You first expose wcf service from your website. From other website they will call that service and get the data and display it to that target website.
Another way you can directly expose method to your web site page, The method you call from your site based on some unique uri. Client web site may call that method with WebClient/HttpWebRequest object(.NET object) and download/get response data from source website and display it to target website. To consume/display data you can use ajax for async communication.
you can visit the following links
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