There are many things you can do to get more visitors to your website, and attract more attention. Some are more important than others... here are my top five (based on over 10 years of web development experience, and running five top-million websites (according to Alexa):
1. Relevant, well-written content
People will link more to content that is well-written or fulfills a need. Then not only do you receive direct traffic from someone else's website, Google picks up on the fact that other people are linking to your content, and your content will have a higher ranking in search results (so, more search traffic as well).
2. Great SEO
Simply adding good page titles, making sure you're using H1, H2, H3 tags and HTML markup correctly, and making relevant links ("more about St. Louis" as a link, rather than "click here" as a link, makes Google much more happy) will help tremendously.
Software like Drupal is built in such a way that Google and other search engines that crawl the web will more easily identify and categorize the content on your site (thus, higher search engine rankings). (Note: I'll be posting a detailed review of setting up one's Drupal site with the RDF + Calais modules soon).
3. Promotion through many channels
Every time a story is posted to our site, it's sent to Facebook and Twitter automatically; this can generate a little extra buzz which gets more visitors as well. But you can't just spam people—you need to respond to questions on FB/Twitter, and use social media to not only disperse, but also gather/respond to information.
In addition to social media, it's important that you provide RSS feeds for content aggregation, email subscriptions (if you can), and consider using technologies like RDFa to allow your content to be spread as widely as possible.
4. Time and Patience
archstl.org has been around since 1998. lifeisaprayer.com since 2004. It takes a VERY long time for a website to get much notice or traffic (unless you're lucky and your site hits digg, slashdot, etc.), and it takes a lot of work to spread the word in a meaningful way—I always put links to relevant articles/content in my forum posts around the web, I pass around my website address when I talk to people, and I leave comments all over the place with my URL in the 'website' field.
5. Content 'gardening'
If a story I have is outdated (not a news item, but something that has more lasting value), I will update the page with more information, reorganize the information in a more meaningful way, and track my logs to see into which pages I should put more time.
(Here's a good example: My Mac is Running Slow - Help! – this page has had over 100,000 page views in a year, mostly due to my updating it with relevant new information over time).
These are just a few tips that I think can help anyone (not just Catholics) get many more times the amount of visitors per month than they are currently getting. I would also include good usability, clean markup, a good URL structure, and fast load times (good site/server performance) if the website is anything more advanced than a simple blog.