Yes, the average library does have shelves full of books... on every subject under (and including) the sun, as well as magazines, movies and music (in varying formats), graphic novels and manga, foreign language materials, and (at least our local library) video games for various gaming consoles. Some also, by way of their websites or computer systems, provide access to ebooks and other online materials.
And yes, most libraries have computer terminals and internet for public use. Printing anything may cost a small fee per page.
Yes, you will likely need a library card, although some provide guest passes to access some services, but library cards are generally free.
Libraries also have librarians who can be wonderfully helpful people. (Treating them with respect helps. A lot.) It's their job to answer questions or help you find the answers. Also to help locate materials in library or help with placing holds on materials or putting in requests for inter-library loans.
Most libraries will also (we love this) purchase recently released books at patrons' request. So if you don't feel you can afford the cover price of a book, request your library get it. You can read it without a hit to your own wallet. Even better, the book is now on the library shelves for others to discover and enjoy.
Libraries also frequently offer programs and events of all kinds, from storytimes for children to public lectures to reading clubs and writers groups.
Seriously, look up your local public library today. If you aren't taking advantage of it, you could be missing something really great.