Templates in Dreamweaver are a bit of a minefield until you get your head around some basic principles.
Unless a region in a page is editable, that is, it has been designated as an area of page content that you are allowed to alter, there's not much you can do with it.
That said, if you open a new page then save it as a template there should be nothing stopping you from putting one or more tables into said page.
Make a new page.
Save it as a template.
From the 'Common' tab on the top toolbar choose the table icon, follow the prompts and add your table.
You can also choose Insert >> Table or just use Ctrl+Alt+T
If your newly added table has no border, either add the border="1" parameter into the table opening HTML tag manually, or click on the table to select it and then add its border value in the peoperties panel along the bottom of the Dreamweaver interface.
If the Properties panel is not visible then either hit Ctrl+F3 or select Window >> Properties from the very top toolbar.
I'm not sure where things are going wrong for you on this one though. If you still get no joy, try posting more information, if at all possible.