The quickest and easiest way is to use google developer tools in Google Chrome.

1st go to google developer tools. F12 or Ctrl+Shift+I or top right Ellipsis->More Tools->Developer Tools

2nd Click on the "Network" tab.

3rd click on the "XHR" sub-tab. XHR(XMLHttpRequest)

if a site uses json it will be listed under the XHR sub-tab. You can search through the different return objects, select one and use the "preview" sub-sub-tab to view it.

Picture json
عنوان: view json
Picture View JSON URL
عنوان: view json url

Although the above way is the easiest it is not the most stable way of getting the info you need. Many sites make changes to the return data without any notice. This will probably break your app...

I think what you are looking for is an API(Application programming interface). Most web APIs return json or xml. You should start by searching for the api documentation for the specific site that you want to get json data from. Example documentation for sites that have public api feeds are github api or youtub api. Many of these will require authentication in order to get the desired json response but the documentation should show you how to do it.

Using a legitimate web api is the most stable way to go. Meaning your app has less chance of randomly breaking all of the time due to feed changes, url changes... I hope this helps!