Cut, copy, and paste.
According to Apple should work as follows:
Find the text you want to edit in a note, email, web page, or other app. You can select a word by double-tapping it, and select more or less text by dragging the grab points. Then tap to cut, copy, or paste. To undo an edit, shake iPhone, then tap the Undo button.
In this example pictured below the text "Photo" nor "No file chosen text" nor even the "Update Status" text on the top of the page can't be selected even on a Mac.
The select-ability of text on a website does depends on the sites implementation details. If a site chooses to disable text selection the iPhone's browser will obey the sites request, and will not give you the ability to select text.
For the Facebook example text is really not select-able even on the Home wall page. If you really want to copy text from Facebook pages try opening the desktop version of the site on your iPhone. The same rings true for other sites that may be offering custom mobile web pages that may limit text selection.