Be active in the community. Make sure people know you (parish wide, not you-you) are Catholic. Have literature on hand.
Have something OTHER than RCIA for people to attend, like a spaghetti dinner and discussion on the basics of Catholicism with Qs and As after, marketing it to lapsed Catholics and non-Catholics. When the local radio station gives the list of activities happening in the area, make sure your church name is always on there with something fun. Put an add in the religion section of the paper.
Go after the kids. If you get the youth, you’ll get the parents too most likely. Recognize what Protestants do well–fraternity, study, and fun.
Make sure you know the people in the parish so that you will recognize any newcomers. (I attended a huge parish in which a newcomer would never go unnoticed; it is possible.)
Have opportunities for fellowship–basketball team, baseball team, knitting group, etc. that people of other faiths (or lapsed) would feel comfortable in attending if invited. Make sure your parishioners are inviting people. On that note, make sure people feel like church is a great place to hang out on non-church time. Have the gym open to the community for basketball or encourage the neighborhood kids to rollerskate in the back parking lot during the day, etc. (Yes, safety is a concern and insurance and blah blah blah, but there are ways to make it work if you want it to.)
Have food! Free food is best. A church I know has a spaghetti dinner with salad and garlic toast once a month where the suggested donation is a couple bucks and the pastor and his family are there; you can just drop in and eat then leave over the course of several hours. A lot of people come back after that because the pastor has an opportunity to tell the person about what is going on in the parish, offer assistance, invite the kiddos to play, etc. Nothing formal. Another church I know has brown-bag casual discussions over lunch and the church provides the cookies for dessert. Another church I know has Wednesday lunch for free on a college campus while discussing their faith and inviting the college kids to attend the church.
Make sure the missals provide explanations on what is happening and when and (briefly) why, and make sure people know where to look to find this information.
The main thing is to connect with the people one-on-one and personally invite them to learn more. The key, though, is to make them comfortable once they get there. Imagine walking into Mass, never having been before, no one there to help you or even to recognize that you exist, and then you leave with no spark of interest in coming back. Not a good scenario.
A better scenario: a person personally invites you to mass, explains some of what to expect, sits with you during mass, then follws up with you afterwards to answer any questions. While there, the priest gives a wonderful homily about the faith. Then in the bulletin/announcements you see that there is an active mom’s group that is always open to new members and a boy scout group going camping and a girl’s choir with open enrollment and a Men’s Night Out. Sounds like a place your family would be happy!
On that note, have open enrollments any place possible. In places where that is not possible, make sure to always note alternatives or the next open enrollment time. It stinks to move into a parish and see that you just missed all the deadlines to get your kids in CCD or your husband in the choir for another full year.