One of the most encouraging spiritual developments in recent years has been the emergence of countless thousands of small Bible study and prayer groups–usually led by lay persons. Many of these cut across denominational lines and are found not just in churches, but in offices, schools, factories, etc.
Begin by getting together with two or three others and asking God to guide you as you make plans together. Think through what your goals are, and who might be the "target audience" for your particular study (e.g., retired people, or young mothers, or single professionals). Think through also how you will publicize it, when it will be best to meet, and how long it should last each week.
In addition, pray that God will guide you to the right passages to study. Perhaps you will study a book of the Bible, or some of the leading people in the Bible, or a particular theme. But be specific, and don't try to do too much. Your local Christian bookstore will have some helpful guides on group Bible studies.
May I suggest you also speak with your pastor about your plans. Let him know you want to be in harmony with the church's other programs and aren't trying to compete with them. Ask his advice also on practical matters such as where to meet, and how to put notices in the church bulletin. Most of all, take heart from God's promise that "The unfolding of your words gives light" (Psalm 119:130).