Well, in the extensions docs, it states in manifest, you would need to include "tabs" as its permission. Same way they explain the hello world application:
Manifest File:
{
  "name": "My Extension",
  "version": "1.0",
  "description": "Opens up a local webpage",
  "icons": { "128": "icon_128.png" },
  "background_page": "bg.html",
  "browser_action": {
    "default_title": "",
    "default_icon": "icon_19.png"
  },
  "permissions": [
    "tabs"
  ],
}
Within the background page, you listen to the mouse click event on the browser action.
chrome.browserAction.onClicked.addListener(function(tab) {
  chrome.tabs.create({'url': chrome.extension.getURL('f.html')}, function(tab) {
    // Tab opened.
  });
});
As you noticed above, you will see that I used the question you saw in the other post. Note, this isn't tested, but I believe it should work.