“My brother is having a hard time finding out if the Church is true. How can I help him?” Liahona, Jan. 2011, 49
Be supportive of him; he needs to feel love—not pressure—from his family. Consider asking him what his concerns and doubts are. Let him finish telling you all of his concerns before you respond. Perhaps his concerns are social or personal, rather than faith-based. You may not be able to provide all the answers he is seeking, but you can reassure him that solutions can be found.
Ask him to pray with you about his worries and encourage him to pray personally about them too. Be sensitive to the fact that it takes some people longer to receive answers than others, especially if they need to sort through things themselves. You could read with him about prayer and gaining a testimony from Alma 32, 3 Nephi 17, or Moroni 10. Also, you could encourage him to speak with your parents, with your bishop or branch president, or with other faithful members of the Church who have worked through similar concerns.
When prompted, bear your testimony to him. Let him know how you feel about the gospel.
Last but not least, remember it is the Spirit who bears witness of the truth. To gain a testimony or to realize that he already has one, your brother must learn to recognize the Holy Ghost. This may take time, and it cannot be forced. You can tell him facts all day long, but it is only through a meaningful connection with the Spirit that he will gain a testimony.
Pray for him and encourage him, support him and listen to him, but remember that he is free to choose. He will choose most wisely by following the guidance of the Spirit.