Whenever I open Microsoft Word 2010, an old document opens up. It's the same one all the time.
And even if I go and try to open a new document, this same document is alway there.
How do I get rid of it?
As I understand it, all Word documents have a default template. The "normal.dotm" template is a blank document which comes up when you start a new document. Check to see if you mistakenly overwrote the normal template with a previous document. Here is some information about Word 2010 templates:
As David suggest in another answer, you have likely overwritten the default template. The simplest way to restore it is:
This article describes how to do that in detail.