I have discussed many strategies for teaching songs, and so far I have left out one of the most common strategies: the one I call "the non-strategy." I don't know what else to call it; it literally means teaching a song without any strategy. How does one do this? Simple. Sing any song slowly and ask your students to sing along with you. Every syllable and vowel will be a hair late, but the song gets sung. With enough repetitions, your group will learn the song.
I do not recommend the non-strategy for most songs, but there are certainly times when the method is perfectly appropriate, particularly when you simply want to have some fun. An admirable goal.
Many songs simply teach themselves because of their simplicity. The joyful repetition in the classic spiritual "This Little Light of Mine" defies teaching. People simply learn it from hearing it. Try these additional verses: "All around the town ... " "Building a new world... " "Free of fear and hatred... " "Sing a song of freedom... " "Sing a song of justice... " "All around this world... " "Life is like a circle... " "I believe in music... " "Harmony of voices... " "Our voices sing together... "
You and your singers can make up a million more verses. Return to the first verse, "This little light of mine" once in a while. If you want, make other changes as you go along. Sing some verses fast, some slow, some loud, some soft. Sing some verses in a blues style or as a lullaby or a rock song or a rap song. Saying you're going to "let it shine" sometimes means letting the creativity shine.