If you created a custom template in Word, you can use it in Word for the web after you save it as a document (.docx file) in OneDrive.
The easiest way to do that is to start in Word on your desktop by creating a document based on your template. Go to File > New, and then click Personal (Word 2013) or My Templates (Word 2010). Then save the document in your OneDrive following these steps in Word.
To use that document as a template, you open it in Editing view in Word for the web, then go to File > Save As, and create a document that's a copy of your template.