It can do all kinds of nifty things, like spell-checking, defining terms, showing stock quotes and weather, doing calculations and conversion...all kinds of things.
In the upper left corner of the Google homepage is a list of more kinds of searches. For instance, if you know you want images or videos, you can click on the corresponding link.
Google also has indexed newspapers from the past centuries and from around the world. Click the "News" link to start searching. If you want to use the archives, click the "Advanced" link to the right of the search box, then the "Archives" link in the center of the page. Some results may have a cost in order to view; these will be labeled "pay-per-view." Honestly, I don't use this feature as much as I probably could.
Two other huge aspects are Google Books and Google Scholar. Both are listed on the "more" pull-down menu. Sometimes you'll run across these when doing other searches, especially if you're looking for a title even if you didn't intend to search for the book itself. The result will start with books.google.com.
Google Books includes works in the public domain plus others that are still under copyright. Thus you won't be able to see full-text for everything. Still, you should be able to view relevant parts or have the option to buy or borrow the book if you do need to see the whole thing. (When you're looking at the content of the book, see the links on the left for obtaining a copy. "Find in a library" will link you to Worldcat.org, which searches library catalogs nationwide to find locations near you that have copies. Talk to your local librarian about how to borrow the book.)
Google presents contents of books (and sometimes magazines) right on the screen. There is usually the option to view it as a PDF, but keep in mind that if the entire book is online the PDF might be huge.
Google Scholar is a little trickier to use. It indexes journals, abstracts, conference proceedings, and other papers, but often these sources are not available full-text for free. There may be a cost to view the contents or the article may not be available online in the first place. Still, you can get a citation and check with your local librarian about getting a copy. For more about searching Google Scholar, see Scholar Help.
Google is a powerful search engine, but it also does so much more. Explore the "more" menu at the top of the homepage to see all the applications Google has to offer.
For the basics of searching Google, see Part 1.