All you need to do is find the library resources you need and click on the links to get to them. When you reach a point where authentication and logging in is required, the library's software will prompt you to log in with your NetID. Only UNR users with a NetID can access most of the library's online resources (ebooks, articles, journals, etc.)
There is also a "proxy bookmarklet" tool that you can install as a bookmark on your browser that will authenticate you directly from a publisher's website. Learn more here.