What we’ve done:
During RCIA I give people a list of different groups and ministries in the parish with names and contact info for leaders. These have been carefully vetted so that it includes only those groups who actually welcome new members. (Unfortunately I have run into some groups that are “closed.” They really don’t want new members and I don’t want to steer people toward them and have them be discouraged.)
I encourage (maybe more like require since if they don’t do it I ask about it frequently) them to visit at least one liturgical ministry and one non-liturgical. For the liturgical ministry the idea is to watch what an altar server/lector/extraordinary minister does during Mass and then talk with one of them to learn more about it – what is involved each week, what kind of training or preparation is required, why does the person enjoy being part of this, what do they get from it, etc. It gives the catechumen/candidate an opportunity to meet and talk with another person in the parish and learn about a way they can contribute afterward.
For the non-liturgical group they attend a meeting with the social justice folks, go with the St. Vincent de Paul folks to meet with someone needing their help, prepare a meal with the people who work with the homeless, sit in on a religious education class or youth group meeting, help with coffee and donuts after Mass, etc. The social justice people have been very welcoming of RCIA folks so that they often end up getting involved even while they’re still in RCIA.
After the catechumen or candidate visits one of these groups they report back at our RCIA session about what they learned. Sometimes what they’ve learned is that particular group is not for them, but they are often very enthusiastic. And that, in turn, inspires others to want to learn more.
In each case, when I’ve talked with the leader of the group about whether they would like to have catechumens and candidates come visit, they’ve been very enthusiastic (except for a couple of groups and I just skip them). These are people who love what they do and want to share it with others.
I see many former RCIA folks at Mass and outside of Mass regularly. Off the top of my head, we have people now who are EMHCs, a member of the parish council, religious education assistants, ushers, a sacristan, a youth group assistant, and members of the social justice group. (As well as some who are happy to attend Mass and not have other responsibilities in the parish.)
I was inspired a lot by Jerry Gallipeau who talks about the apprenticeship model in RCIA. You learn by doing.