I have a family member who is an agnostic. How should I approach him about coming into the Church?
Unfortunately, there is not a “one-size-fits-all” approach to evangelization. You have to first discern the particular issues that concern your family member and tailor your apologetic approach to those issues. In the meantime, here are some helpful resources:
Eternal Gamble** by Jimmy Akin
Authority and the Adventurer by G. K. Chesterton
Handbook of Christian Apologetics by Peter Kreeft and Ronald Tacelli, S.J.
Search and Rescue by Patrick Madrid
How NOT to Share Your Faith by Mark Brumley