Show Number of Words in Microsoft Word
Among other types of document information, you can display, anywhere you like, the number of words in Word document by using a field.
From the menu, choose InsertField. From the Categories drop-down, choose Document Information. Then choose NumWords from the Field names and your desired format (likely the one shown in the graphic).
As with all fields, this one doesn't automatically update. You may need to force the field to update if you want to watch the word count grow. See this article for more information.