The trick is that you need to modify the "Normal" style that's defined in the Normal TEMPLATE.
What many people don't realize is that when you create a new document, Word pulls the settings for that document (including style definitions) from the Normal template. So if you re-define the styles there (in the template), then your new documents will inherit those styles. The template you want - Normal.dotm - is buried fairly deep, so it can be a challenge to locate. Here's how...
Using Word's menus, open the template: File menu > Open...
Navigate to [user name]/Library/Application Support/Microsoft/Office/User Templates/Normal.dotm and open that template.
(Note: Don't drill down in the Finder to locate that template in it's folder and then double-click it....that won't open the template itself, it will just open a new blank document and you won't be redefining the style in the template).
Note that the document title (at the top of the document window) should say "Normal.dotm", not "Document1".
With the Normal.dotm template open (it just looks like a blank document), click Format > Style...
In the Styles box, click "Normal" (it should already be selected by default, but make sure that's the style you've got selected), then click Modify...
In the Modify Style dialog, click the Format pop-up menu in the lower left corner and click Paragraph...
In the Paragraph dialog, click the Indents and Spacing tab at the top (again, it should already be selected by default, but make sure that's the tab you've got selected), and then under Spacing, change the "After" setting from 10 pts (the default) to 0 pts. This will redefine the Normal style so there is no extra space between the paragraphs.
Click OK a couple times to close the two dialogs; when you get back to the Style dialog, click Apply.
Back in your Normal.dotm template document (which should still appear blank), click the Save button or File > Save.
Quit out of Word (Word > Quit Word).
Relaunch Word, create a new document, type some stuff, hit Enter/Return, and enjoy your nice, tight paragraph spacing.
Hope that helps.