I have always found it difficult to do this. Supposedly you can click Tools, select Templates and Add-ins (at least in Word 2000), select the template (normal in your case), and tick the option automatically update document styles. Click OK.
Then just edit your document. Save it in the normal way as a .doc file, but styles changes will be made to normal.dot as well (and if prompted, confirm changes to normal.dot). Then go back to the Tools menu and deselect the option mentioned above.
The way I do it, is to open a blank document. Make the necessary style changes. Save it as a .doc file, e.g. normal.doc. Close Word. Locate the normal.dot file on the computer. Either delete it, or rename it. Then rename normal.doc to normal.dot and move it to the folder where it should be. Then next time you open Word, the new normal.dot will take effect. With this method, I find I have a better idea of what I'm doing.