Aside from our many fabulous print resources, you can access Ancestry Library Edition for free when you’re inside any of the three UAPL branches. But if you’re interesting in doing your research from home, there are plenty of great, free online resources!
Have you tried the new HeritageQuest? Recently purchased and updated by Ancestry, it's much easier to use. If you’re new to genealogy, there are several Research Aids to guide you through the first few steps of online research (although it certainly helps to talk to your family first!). Heritage has census records, but they also have a huge and searchable collection of local history books and periodicals.
There are also some great websites worth a look. Cyndi’s List is a collection of useful websites for genealogists subdivided into helpful categories. You may also find a great deal of information at FamilySearch.org, a popular genealogy website.