The article “Inviting Success” in the March 2014 Ensign gives 10 suggestions for sharing the gospel:

1. Strike up a conversation. As you are getting acquainted, it’s natural to let people know you’re a member of the Church. Simple statements like, “I’m a Latter-day Saint, but many people know us as Mormons,” can open the door.
2. Talk while traveling. Visit with fellow travelers on the bus or plane or with families you meet at vacation spots. One man made it a point to ask taxi drivers about their family and then discuss family home evening.
3. Refer friends to Mormon.org. This website is a great place for those unfamiliar with the Church to get to know it better.
4. Invite your friends to chat with the full-time missionaries online or in person. On Mormon.org, people can have conversations with missionaries. And of course you can always introduce people to the elders or sisters in your area.
5. Use social media. The Church provides an array of opportunities to like or share content online, including memes, quotes, and videos. Hashtags (a word or group of words tagged with #) also enable people to follow web conversations about the Church.
6. Share videos. Become familiar with videos on Mormon.org and biblevideos.lds.org. Watch them with friends or share links. Also mention Mormon Messages, which offer inspiring answers to life’s questions.
7. Share cards and posters. Pass-along cards and posters allow you to share inspiring ideas (see cards on page 29 of the October 2013Friend, for example). [Also, learn how to make personalized pass-along cards from Mormon.org.]
8. Ask the missionaries. Invite your friends to read “Ask the Missionaries! They Can Help You!” by Elder Russell M. Nelson of the Quorum of the Twelve Apostles.
   
9. Attend a temple open house. Let people know about the marvelous opportunity to attend the open house prior to a temple dedication. Offer to go with them.
10. Reach out to those who are returning. Home teachers and visiting teachers have a great opportunity to be missionaries to less-active members, who in turn know others who may be receptive to the gospel.