You are the leader. Determine to help improve the corporate worship experience week by week by truly leading and encouraging the people to sing.
If you have ever sung in a choir, this may help. Think of the congregation as the choir and you are the choir director. Decide in advance what you expect musically from the congregation. Unlike a choir, you do not have a separate rehearsal. Instead, each worship service is the choir performance.
Introducing new songs. Decide when is the best time to teach the congregation. Determine how many weeks it will take before the congregation fully embraces the new song, then, strategically plan how you will teach the new song. (If what you normally do works, then great. If not, ask other worship leaders how they teach new songs.) Teach the new song to a small group or your worship team and look for their response. Tell the congregation about the new song and encourage them to listen to it in advance on iTunes or YouTube.
Men Only. Women Only. This is good to change up a familiar song, but don’t use this method too often. It allows a time of silence for half of the congregation which will help them focus on the lyrics and literally worship without using their voices.
Dynamics & Tempo. We often sing joyful songs loud and intimate songs soft. As the leader, you can mix it up. Lead the people to sing the chorus soft this time (and maybe slower). Tell them to consider the words (lyrics). You may also want to read or quote a scripture that parallels the lyrics.
Unison & Parts & A Cappella. This is effective on songs like “Amazing Grace” and other very familiar songs. Tell the congregation you want everyone to sing the first verse in unison, then if they can sing a part, to do so on the next verse. Then, while everyone is singing parts, drop out all the instruments. Be sure to encourage the congregation to “sing out”. You are the leader and they will respond if you lead them.