There are lots of genealogy sites.  Some have free information.  Type in search terms like "irish genealogy" or "beginning genealogy" or "free genealogy online".  You can try searching your name, or their name, on Yahoo or Google and see if some one of your distant relatives has already posted a family tree online.  You might be surprised what you find.

Here is a link to a posting I found doing a search on Yahoo for Ann Worden.  born in 1855:  http://homepage.mac.com/graememoad/Family3/PS03/PS03_367.HTM

or this one:  http://users.bscn.com/~harryv/worden.htm