YEAH.. Every Church should have a site now-a-days. I'm shocked your parrish doesn't
Since you used the word "parrish" your probably Catholic or Lutheran, since they are the ones who use that terminology the MOST.
A website will make it easier for people to look up information, since many 30yr olds and under think of the 'web FIRST and the yellowpages a distant 3rd or 4th. HECK, I'd probably search the web, then dial 1-800-Goog411 to get their number and listen to a recording, and ONLY THEN, even THINK about referring to the information in the yellowpages.
A Website ALSO allows them to be more wordy about what they say. They can include all sorts of special announcements, Prayer requests, a Weekly or Monthly BLOG of the priests. They can have people opt into newsletters which they use to electronically send out emails with announcements like "Please pray for Susie's Heart Surgery" and stuff like that.
Make sure you tell them stuff like that if they need convincing.
PERSONALLY .. I'd post questions in the Computer and Internet / section of Yahoo Answers if you need help.
I suggest using a Content Management system so that Staff at your parish can update the site without having to edit HTML code.
Something like Plone, Joomla, or Mumbo, are free and open source.
My Dad sets up Websites for small businesses and he uses Joomla so that once their setup, the owners of the business can access the site and update their own pages or create new one.
Some Internet Providers give you their OWN content management system if you design your site using their tools, but PERSONALLY I don't think they are as good as dedicated CMS like Plone, Joomla, Mumbo, etc.
A GOOD Content system allows you to delegate access to each page so that 1 person can have rights to 1 page but you can block their access to make changes on other pages, etc. You can also have changes made sent to an "approver" who then accepts the changes, thus making them active on the site.
::EDIT:: YEAH, Drupal - that's a another good one. Thanks for reminding me. I'm sure there are a bunch I don't know of, but those are the BIG, free, op-source CMS.
Please please, I beg of you, don't create it in MS Front Page or other "What you see if what you get" stand alone applications. Those things create TERRIBLY bloated pages that are un-editable by normal humans. -- If you're a web designer.. then I'm preaching to the choir, 'cause you already know that.
Anyways...
God Bless and Wish ya Luck!