How can I find Nielsen ratings for specific television shows in a given time period?
Several sources on the Web list the top twenty or so Nielsen-ranked television shows for the current week; the best may be http://tvbythenumbers.zap2it.com/category/overnight-tv-ratings/tv-ratings-nielsen-overnight-tv-show-ratings/ which also lists separate rankings for such categories as sports shows, syndicated shows, cable shows, etc., and has an archive back to 1997.
The Minneapolis STAR TRIBUNE (Wilson Library Newspaper Room) lists the top television shows of the previous week in each Thursday "Variety" section, and other newspapers and news magazines may also publish variants of such a list.
Annual almanacs such as the WORLD ALMANAC (available at most reference desks) or the TIME ALMANAC (Wilson and Magrath reference desks) include lists of the top-ranked television shows of the previous year in each edition (numbers and breakdowns vary).
All of the above information is available free in one form or another. Nielsen Media Company also collects much more elaborate and comprehensive data on rankings by local market, by narrow demographics, etc. Circulation of Nielsen publications reporting this data is tightly controlled by the company, and is not available to libraries or, generally, to anyone other than Nielsen's clients.