As a homeschooler, I bet you would be surprised to find that we do not frequent the library. Between encountering people viewing questionable websites, to rowdy bunches of kids after school and even during school hours, it is not a great place to be. Then there is the problem of my kids losing books in the house and causing large library bills.
Still, this does not make the library irrelevant for us. The public library provides many online resources that you can access with your library card number and password. Here are some of the things that most libraries provide to their patrons online:
In my state, we have Galileo (the Digital Library of GA) which provides a digital library of books, manuscripts, photographs, government documents, and more. Most states have a similar system.
In addition, we have access to World Book Encyclopedia websites, newspapers, Gale Business and Resource Center, Genealogy websites such as Heritage Quest and Ancestry Library Edition and Ancestry Library.
One site that is of particular good use to homeschoolers is LearnATest test preparation websites by Learning Express Library. This includes the Success in 20 Minutes a Day series that you can practically teach high school and college prep courses from. Yes, they serve as a FREE curriculum.
The Wilson Web website is a full Biography reference where you can learn about anyone in history and several other history databases.
You can also find access to many science and medical databases through the public library websites. The number of resources is endless.
Since many libraries have the same resources and subscriptions, you should be able to find all that I mentioned here and more to help you in your homeschooling journey.