Search Site 3.2 allows you to search within the current site from the search bar, or from the context menu, or by drag-and-drop into the search bar. This makes it easy to do a website-specific search, using the search engine currently selected in the search bar, if the site doesn’t have its own search box. If you use the search bar, type the search terms into the search bar and then click on the Search Site icon that appears in the search box or press Ctrl+Enter.
Searching the current site can also be done by using the right-click (context) menu. Just select the word or words you want to search and select Search Site for selection in the context menu. Unfortunately, the search results do not automatically open in a new tab, you must hold down the ctrl key as you select the Search Site for selection context menu item. Using the ctrl key will move the results to the foreground tab or if using the search bar, hold down Ctrl when clicking on the Search Site icon to display the results in new foreground tab.
I also recommend selecting Enclose the selected text in quotes when searching from context menu in the Options Dialog.