One main purpose of Christian adult groups is to strengthen your faith in God and encourage each other to grow spiritually so you can become mature in your lives. When Christians fellowship together, they develop a strong bond that will get them through the toughest times in life, and this is how God wants his followers to interact with each other. You could have the group meetings at your home, a church, or coffeehouse depending on the size of your group. It's also beneficial to have a time of prayer before starting activities so you'll have God's wisdom and protection throughout the meeting.
One good activity is to have a weekly book club in which you read books that are biblically sound and which relate to issues in Christianity. You could assign a certain book each week to group members and have them write down discussion questions to help facilitate the conversation. Also tell members to bring their Bibles as well as the assigned books so that you can examine whether the author's views are in agreement with it.
Engaged Couples' Group
If your church has a lot of engaged couples, you could start an engaged couples' mentoring group if you're a married couple. Talk to the engaged couples about what the Bible has to say about building a good marriage. You can also share your experiences as a couple so they'll get a realistic view on both the ups and downs of married life.
Incorporate some fun into the group meetings by playing a trivia game. One idea is to hold a game in which you'll ask members what the Bible has to say about specific contemporary issues that Christians deal with. For example, you would write questions on index cards such as "What does the Bible have to say about child discipline?" The member who gives the most accurate answer from the Bible will get a gift card for a prize.