The warning language and the steps needed vary over time. Basically, you can assume that resources reached through links on the library website are safe and take the steps needed to "accept the risks" or "add exceptions.
Here are the steps that are needed to gain access to several library resources when the Firefox "Secure Connection Failed" warning appeared in 2011.
1) When the "Secure Connection Failed" message appears while you are trying to access a Library resource, click on the "Or you can add an exception" link.
2) The display will change slightly. Click on the "Add Exception" button that appears.
3) The "Add Security Exception" dialog box will appear. Click on the "Get Certificate" button.
4) The display will change slightly. Click on the "Confirm Security Exception" button.
