Very important note:

Only Word can create a (complete) normal template. You cannot take a document and save it as normal.dotm and have a fully functional normal template.

You can open the normal template created by Word and change the styles in that template. Then, save that template. How to Open the Normal Template

You can also use a different template, not the normal template, as the basis for new documents by default. This isn't simple, but it can be done. An example is Easy New Document Template Package.

You can set up a template to hold styles for other documents that is not the normal template but which is used as a resource. A Global StyleSheet in Microsoft Word?

You can also use other templates as the basis for new documents by choosing those templates when creating documents. These are called document templates and are stored in one of the template folders described in my article on templates. Access to thes is further explored in File New Variations in the Versions of Word