Start by planning where you'd like to hold meetings. Decide where you want to have the book club. Consider the size of the space where you'll be meeting. There may be a meeting room at your church your pastor will let you use.
Think about who you'd like to be in your club. A consistent group of five makes for a more productive, cohesive book club, than a very large club with very occasional members. Who will you recruit and from where? Would you prefer a group of your close friends? Do you want to include family members? Or, do you want to keep it to your church? Another alternative, if your goal is to meet new Christians, you might want to open up membership.
Cap membership and get a commitment from everyone who says yes. Even those with the very best intentions can take on too much and your book club membership will suffer. Are you going to allow members to invite others? In your original invitation (which can be a follow up to a phone call, especially if you want initiate contact "in person") -- it should be written, via email is the easiest way these days. Let them know that while everyone has to miss a meeting here and there, that you hope that they'll set that time aside for your Christian Book Club. Your membership may be directly tied to the space you're using.
Be consistent right from the start. Will the meetings always be held at your house or the church or ? Once that's established, decide what day and time you want to hold it and keep to that day (or night) and time. Logically, you will probably want to meet every four to six weeks to give members time to read the book.
Decide how you will choose books. Will you let members make suggestions? It is, your club, after all, and if you want, you can actually choose the books you want. However you decide, you should know what the next book will be by the current meeting. Make the announcement of the next book.
Send out an email or an Evite to each member. Require they rsvp by at least a week before that next book club meeting. Include in that email or Evite a way for members to tell you/other club members to let you know (if you do potluck) what they're bringing.
Serve food and drink. Potluck is a great way to do it. One book club based in Culver City tries to choose their "Eats" (as they call the book club food) with some relation to the book. For example, if they were going to read Memoirs of a Geisha (not likely reading for your Christian book club), they each bring something Japanese; when they read Persuasion (an ideal book, a classic) for your Christian Book Club, they held an English tea.
Prepare topics for discussion. Your Christian Book Club is likely to evolve as time goes by, but in starting, it's best to keep it organized. It's up to you to keep the ball rolling/conversation going.
Set a cap (eg, 2 to 4 p.m.) for how long the meetings will run so that everyone (and you) are able to make plans appropriately. It's a thoughtful way to run a Christian Book Club.
Choose a book or books. There are so many Christian/faith-based books these days, and they span the genres. You can find Christian historical novels, historical romances, suspense thrillers, chick lit, family stories, you name it.