On the front page of Ancestry.com you can click on the free 14 day membership. You can search the site for 14 days at no cost to see what you find. However you must provide a credit card number when you sign up and it will be charged if you do not cancel prior to the end of your trial period. If you use this method try to make sure you will have the time to devote to your research in those 14 days so you can take full advantage of the free trial period.
Ancestry.com allows you to sign up for a quarterly membership instead of an annual one. This works out to be a more expensive that an annual membership if you pay for a whole year in quarters, but you are only committing for 3 months at a time. You can change to annual if you decide to keep the subscription long term. Many libraries have institutional memberships to Ancestry.com (as well as other paid subscription sites). It is my understanding these accounts are slightly different from personal ones. For example you cannot create a personal family tree on the library account. But this is a great way to try out the site at no cost.
Finally, if you do not want to pay for any subscription sites there are alternatives.
LibrariesMost larger libraries have the census years on microfilm.
Many have access to Heritage Quest. HQ lets you search the census, books, and other databases. Some libraries offer home access to Heritage Quest with a current library card. If your local library does not offer home access check the libraries in surrounding towns. It can be worth the trip to sign up for a card to gain access to Heritage Quest from home.
Roots Web Search SiteThis site has lots of links to general genealogy information, family trees, plus other databases. You can also search Roots Web by your ancestor's name in numerous databases at once. A few of the databases on Roots Web are the SSI Death Index, Death Indexes for various states, Family Trees, Obituaries (most are current), and many more.
FootnoteTo access all their records you do need a paid subscription. However they offer a free membership which allows you to view various records. Footnote varies the databases offered in the free membership (as a promotion). So it pays to check back with them occasionally to see what currently is available at no cost. They do let you get a snippet of the records that require payment. If you find anything interesting many libraries have memberships for Footnote which you can access for free from the library.
Also you can check out my Free Links page, I will be adding new links on a regular basis.