It sounds like you're being forced to use ASP.Net Web forms. I'd typically recommend you use ASP.Net MVC instead, and it does support Master pages, but really everything is a view, and I expect you would get push-back from the professor. So, to keep with the standard ASP.Net Web forms approach, you should create a new ASP.Net WebSite, and check off that you want a master page. Then Visual Studio will create the Master page for you, and any new aspx pages you create you can click a box to have them inherit from the master page.
If you look at the .Master page, you'll see the same HTML you would see on any site, including the , and tags. You should just include the .css file that contains your 960 framework file, just like you would on any Web page. Then the rest f the page will use the 960 grid, and you can put the necessary col# classes inside the class tag (or CssClass for ASP.Net controls) to get the display to work correctly.