You can always access Ancestry Library Edition for free while you're in the library but when you're at home and don't have a subscription to Ancestry, there are free resources you can access through their site.
You can search Ancestry's Free Index Collection. Search through selected collections of indexes. You may not always be able to view full records without a subscription but you can still find some great information.
You don't need a paid subscription to create a family tree on Ancestry. Upload information about your family and Ancestry will give you "hints" of records that might be applicable to ancestors; however, you'll need a subscription to view the full record.
And you can always take advantage of Ancestry's Learning Center. Videos and research guides can help you further your research.