Instead of just using the mouse to select text and move around within a webpage, you can in fact use the standard navigation (arrow and page-) keys on your keyboard to do this, making in particular specific text selection far more targeted and easier to achieve.
This particular browse mode is referred to as Caret Browsing, named after the caret (the cursor icon) which appears when you edit a text field like in a Word document for instance.
To activate this mode in either FireFox or Internet Explorer 8, simply press the F7 key. This will pop up the following dialog, which if you agree to, switches on the caret browsing mode.
To turn caret browsing off, simply press F7 again.