How do I enable "track changes" in Microsoft Word?

The feature you're talking about is "change tracking" though most people I know call it "revision tracking". Same thing. To enable it, you simply select "highlight changes" from the "change tracking" option under "Tools":

Once you've done that, it pulls up a small dialog box that gives you access to the critical setting:

As you can doubtless guess, the key box to check is "Track changes while editing". Now the program is keeping track of any tweaks you -- or anyone else in your organization -- makes. Usually you'll want to show the changes on screen and with printouts, but you can turn that off, as you can see, and it still keeps track of everything. Very useful.

Now, when you add or delete material, it shows you visually what's happened:

This is the old style revision tracking, actually. You might start out with "edit balloons", which some people prefer, but I like the old style because it lets you have more of the document on screen. You can switch between them by clicking on the "Options..." button on the earlier dialog box. The key setting is "Use balloons to display changes". Try both, see which you prefer!

When you're done with all of your editing, don't forget to accept the changes, either en masse or stepping through them one-by-one by using "Accept or Reject Changes..." off the Tools --> Track Changes menu, as shown above.