The aim of the main search page (http://churchrecords.irishgenealogy.ie/) is to provide a simple entry point. Beware of entering too much information. A forename and surname are generally enough. Then examine the results. The navigation links in the left-hand column allow you to narrow down these results by denomination, by event, and by decade. At the bottom of the left-hand column, you can also add in additional names to further narrow a search.
You should be aware that by default the search returns all records in which both personal names occur. In other words, if you enter "John Murphy", the search will give you all records in which a "John" and a "Murphy" (or their variants) occur in any of the name fields. So, for example, if the father's name is John and a godparent's surname is Murphy, that record will be retrieved by a search for a John Murphy. You can sort the results by relevance to show most precise matches first. You can also sort the results in simple chronological order.
The overall moral is simple: cast your net as wide as possible to begin, than systematically narrow down the results.