Once you're in Nexis Uni, click "Cases" in lower left under the Guided Search area to search for a legal case (or cases about a certain topic). Use the search box to the right of "Which Jurisdiction?" (do not use the larger, main search box). For state case law, you'll also be asked to enter in a state name.
Select the Jurisdiction and enter the citation in the search box (under "...about"), and click Search. The problem with searching by title in some cases is that cases are often cited in other cases. So you will get search results other than the actual case you want. What you can do is look up the case at the Legal Information Institute - and get its full title. Or you can get its case citation (i.e., 159 U.S. 533) and look it up by that.
Use the Main search box and click 'All Content Types" in right side box and select 'Legal' from drop-down. Select a country from the "Legislation" Category list.
You can also browse or search within New York State Consolidated Laws and Constitution material here: http://codes.findlaw.com/ny/