You expect that their language, their customs, and their beliefs will be different from yours. You begin by listening, so that you can learn the culture, better to relate Jesus to the people. You are prepared to make cultural mistakes, so you learn to laugh at yourself. You listen for the cultural equivalents of hospitality, adoption, heaven, health, and a thousand other things that the Bible commends but whose cultural representations will be unfamiliar to you. Most importantly, you will want to continue a love relationship with Jesus Christ.
Love is a universal language, welcome in any culture.
Love is the hallmark of a Christian. I submit that this too is a cross-cultural experience for Evangelicals today, and that the way to minister is the same. Find cultural equivalents. Avoid language that is misunderstood in ever-changing gay culture. In short, love.