You will probably encounter sincere, intelligent, well-intentioned people who will make good arguments about why they believe the way they do. This can be confusing and frustrating. Before you start talking to people, you need to prepare. The thing that helps keep me centered is having a testimony of the plan of salvation. Focusing on the plan of salvation allows me to keep the right spirit and to remind myself that I am motivated by a conviction of the truthfulness of the plan of salvation as opposed to a need to prove the "wrongness" of homosexuality.
One of the greatest challenges in talking about homosexuality is the tendency to speak in terms of moral relativism. Moral relativists would have you believe that God's commandments are only one way of looking at the world and that there are other viable alternatives. These arguments can be very persuasive, but they are spiritually deadly. Consider the following vignette from Elder Hales of the Quorum of the Twelve Apostles:
In the premortal existence, ours was not a selective obedience. We did not pick and choose which parts of the eternal plan to follow. I learned that lesson on our first night flying solo in pilot training when all of us were given the instruction: “Don’t fly acrobatic patterns at night. You are beginning pilots without instrument flight training.” Some time later, an otherwise good pilot and a great friend chose to disobey that command. As he flew loops and barrel rolls through the night sky over Texas, he looked through the cockpit canopy and thought he saw stars above him, but he was really seeing the lights of oil rigs below. He was experiencing vertigo: the g-forces on his plane made it seem he was right side up, yet he was upside down. As he pulled up on the stick to climb higher into the night sky, he dove toward the earth and crashed into the twinkling lights of the oil field below.
When you are flying an airplane, if you change your position by just one degree at a time, your inner ear cannot detect the change. Brethren young and old, when we practice selective obedience, we change our position relative to the Lord—and usually by only one degree at a time. As the deceptive forces of the adversary work on us, we cannot detect them, and we experience spiritual vertigo. While it may seem like we are going in a safe direction, we are in fact headed for disaster. In the preexistence, our decision to follow the Lord was all-or-nothing. Following that pattern through our mortal probation will get each of us back to our Heavenly Father.
Robert D. Hales, Ensign May 2007
Once you have firmly established your personal testimony of the plan, you should research the specifics of the plan as it relates to marriage. In order to advocate for the church's position on marriage, you must be current with what the brethren are teaching. Reading selected quotes from out-dated materials may undermine your efforts, not because our doctrine has changed, but because we know a great deal more about same-gender attraction than we did 30 years ago. A lot of research has been done since the "Miracle of Forgiveness" and we should recognize that. Three resources that I find invaluable are found linked below:
The Family a Proclamation to the World.
This document was put out by the First Presidency and the Quorum of the Twelve Apostles in 1995. It states very clearly the doctrines of the church as they relate to God's plan for families. This should be your primary resource as it is still viewed as the authoritative position of the church on a variety of family related issues.
An interview with Elder Oaks on the subject of same-gender attraction.
As both an Apostle and a legal expert, Elder Oaks provides the most well-articulated answers to some of the toughest questions that you can expect to come across. I think this is a must read.
God Loveth His Children.
This is a resource that was mailed to bishops in 2007. It will help you understand how the church counsels its members who struggle with the challenge of same-sex attraction. It affirms the importance of each member in the church and reassures us that we are judged by the Lord based on how we handle our temptations (versus what our temptations are).
These are my top 3 resources. There are many others available here under the topic of same-gender attraction.
Part II. What to say and how to say it