How to get the currently opened tab’s URL in my page action popup?

Use chrome.tabs.query with the following parameters:

• queryInfo object:
  • active: true – To get the active tab
  • lastFocusedWindow: true – To select the active window
• callback function:
  This function receives one argument: An array of matched tabs. Since only one window can be active, and one tab within this window, the array has only one element. This element is an object with the Tab signature.

Code snippet:

// Do NOT forget that the method is ASYNCHRONOUS
chrome.tabs.query({
    active: true,               // Select active tabs
    lastFocusedWindow: true     // In the current window
}, function(array_of_Tabs) {
    // Since there can only be one active tab in one active window, 
    //  the array has only one element
    var tab = array_of_Tabs[0];
    // Example:
    var url = tab.url;
    // ... do something with url variable
});

The activeTab permission is sufficient for this to work.